Help for package bsvars

Type:

Package

Title:

Bayesian Estimation of Structural Vector Autoregressive Models

Description:

Provides fast and efficient procedures for Bayesian analysis of Structural Vector Autoregressions. This package estimates a wide range of models, including homo-, heteroskedastic, and non-normal specifications. Structural models can be identified by adjustable exclusion restrictions, time-varying volatility, or non-normality. They all include a flexible three-level equation-specific local-global hierarchical prior distribution for the estimated level of shrinkage for autoregressive and structural parameters. Additionally, the package facilitates predictive and structural analyses such as impulse responses, forecast error variance and historical decompositions, forecasting, verification of heteroskedasticity, non-normality, and hypotheses on autoregressive parameters, as well as analyses of structural shocks, volatilities, and fitted values. Beautiful plots, informative summary functions, and extensive documentation including the vignette by Woźniak (2024) <doi:10.48550/arXiv.2410.15090> complement all this. The implemented techniques align closely with those presented in Lütkepohl, Shang, Uzeda, & Woźniak (2024) <doi:10.48550/arXiv.2404.11057>, Lütkepohl & Woźniak (2020) <doi:10.1016/j.jedc.2020.103862>, and Song & Woźniak (2021) <doi:10.1093/acrefore/9780190625979.013.174>. The 'bsvars' package is aligned regarding objects, workflows, and code structure with the R package 'bsvarSIGNs' by Wang & Woźniak (2024) <doi:10.32614/CRAN.package.bsvarSIGNs>, and they constitute an integrated toolset.

Version:

3.2

Date:

2024-10-24

Maintainer:

Tomasz Woźniak <wozniak.tom@pm.me>

Imports:

Rcpp (≥ 1.0.7), RcppProgress (≥ 0.1), RcppTN, GIGrvg, R6, stochvol

Suggests:

knitr, tinytest

LinkingTo:

Rcpp, RcppProgress, RcppArmadillo, RcppTN

License:

GPL (≥ 3)

URL:

https://bsvars.org/bsvars/

BugReports:

https://github.com/bsvars/bsvars/issues

Encoding:

UTF-8

LazyData:

true

VignetteBuilder:

knitr

RoxygenNote:

7.3.2

NeedsCompilation:

yes

Packaged:

2024-10-24 11:54:34 UTC; twozniak

Author:

Tomasz Woźniak

[aut, cre]

Depends:

R (≥ 3.5.0)

Repository:

CRAN

Date/Publication:

2024-10-24 14:30:05 UTC

Bayesian Estimation of Structural Vector Autoregressive Models

Description

Provides fast and efficient procedures for Bayesian analysis of Structural Vector Autoregressions. This package estimates a wide range of models, including homo-, heteroskedastic and non-normal specifications. Structural models can be identified by adjustable exclusion restrictions, time-varying volatility, or non-normality. They all include a flexible three-level equation-specific local-global hierarchical prior distribution for the estimated level of shrinkage for autoregressive and structural parameters. Additionally, the package facilitates predictive and structural analyses such as impulse responses, forecast error variance and historical decompositions, forecasting, verification of heteroskedasticity and hypotheses on autoregressive parameters, and analyses of structural shocks, volatilities, and fitted values. Beautiful plots, informative summary functions, and extensive documentation including the vignette by Woźniak (2024) <doi:10.48550/arXiv.2410.15090> complement all this. The implemented techniques align closely with those presented in Lütkepohl, Shang, Uzeda, & Woźniak (2024) <doi:10.48550/arXiv.2404.11057>, Lütkepohl & Woźniak (2020) <doi:10.1016/j.jedc.2020.103862>, Song & Woźniak (2021) <doi:10.1093/acrefore/9780190625979.013.174>, and Woźniak & Droumaguet (2015) <doi:10.13140/RG.2.2.19492.55687>. The 'bsvars' package is aligned regarding objects, workflows, and code structure with the R package 'bsvarSIGNs' by Wang & Woźniak (2024) <doi:10.32614/CRAN.package.bsvarSIGNs>, and they constitute an integrated toolset.

Details

Models. All the SVAR models in this package are specified by two equations, including the reduced form equation:

Y = AX + E

where Y is an NxT matrix of dependent variables, X is a KxT matrix of explanatory variables, E is an NxT matrix of reduced form error terms, and A is an NxK matrix of autoregressive slope coefficients and parameters on deterministic terms in X.

The structural equation is given by:

BE = U

where U is an NxT matrix of structural form error terms, and B is an NxN matrix of contemporaneous relationships.

Finally, all of the models share the following assumptions regarding the structural shocks U, namely, joint conditional normality given the past observations collected in matrix X, and temporal and contemporaneous independence. The latter implies zero correlations and autocorrelations.

The various SVAR models estimated differ by the specification of structural shocks variances. The different models include:

homoskedastic model with unit variances
heteroskedastic model with stationary Markov switching in the variances
heteroskedastic model with non-centred Stochastic Volatility process for variances
heteroskedastic model with centred Stochastic Volatility process for variances
a model with Student-t distributed structural shocks
non-normal model with a finite mixture of normal components and component-specific variances
heteroskedastic model with sparse Markov switching in the variances where the number of heteroskedastic components is estimated
non-normal model with a sparse mixture of normal components and component-specific variances where the number of heteroskedastic components is estimated

Prior distributions. All the models feature a Minnesota prior for autoregressive parameters in matrix A and a generalised-normal distribution for the structural matrix B. Both of these distributions feature a 3-level equation-specific local-global hierarchical prior that make the shrinkage estimation flexible improving the model fit and its forecasting performance.

Estimation algorithm. The models are estimated using frontier numerical methods making the Gibbs sampler fast and efficient. The sampler of the structural matrix follows Waggoner & Zha (2003), whereas that for autoregressive parameters follows Chan, Koop, Yu (2022). The specification of Markov switching heteroskedasticity is inspired by Song & Woźniak (2021), and that of Stochastic Volatility model by Kastner & Frühwirth-Schnatter (2014). The estimation algorithms for particular models are scrutinised in Lütkepohl, Shang, Uzeda, & Woźniak (2024) and Woźniak & Droumaguet (2024) and some other inferential and identification problems are considered in Lütkepohl & Woźniak (2020).

Note

This package is currently in active development. Your comments, suggestions and requests are warmly welcome!

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Chan, J.C.C., Koop, G, and Yu, X. (2024) Large Order-Invariant Bayesian VARs with Stochastic Volatility. Journal of Business & Economic Statistics, 42, doi:10.1080/07350015.2023.2252039.

Kastner, G. and Frühwirth-Schnatter, S. (2014) Ancillarity-Sufficiency Interweaving Strategy (ASIS) for Boosting MCMC Estimation of Stochastic Volatility Models. Computational Statistics & Data Analysis, 76, 408–423, doi:10.1016/j.csda.2013.01.002.

Lütkepohl, H., Shang, F., Uzeda, L., and Woźniak, T. (2024) Partial Identification of Heteroskedastic Structural VARs: Theory and Bayesian Inference. University of Melbourne Working Paper, 1–57, doi:10.48550/arXiv.2404.11057.

Lütkepohl, H., and Woźniak, T., (2020) Bayesian Inference for Structural Vector Autoregressions Identified by Markov-Switching Heteroskedasticity. Journal of Economic Dynamics and Control 113, 103862, doi:10.1016/j.jedc.2020.103862.

Song, Y., and Woźniak, T. (2021) Markov Switching Heteroskedasticity in Time Series Analysis. In: Oxford Research Encyclopedia of Economics and Finance. Oxford University Press, doi:10.1093/acrefore/9780190625979.013.174.

Waggoner, D.F., and Zha, T., (2003) A Gibbs sampler for structural vector autoregressions. Journal of Economic Dynamics and Control, 28, 349–366, doi:10.1016/S0165-1889(02)00168-9.

Woźniak, T., and Droumaguet, M., (2024) Bayesian Assessment of Identifying Restrictions for Heteroskedastic Structural VARs.

Examples

# upload data
data(us_fiscal_lsuw)    # upload dependent variables
data(us_fiscal_ex)      # upload exogenous variables

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1, exogenous = us_fiscal_ex)

# run the burn-in
burn_in        = estimate(specification, 5)

# estimate the model
posterior      = estimate(burn_in, 10)

# compute impulse responses 2 years ahead
irf           = compute_impulse_responses(posterior, horizon = 8)

# compute forecast error variance decomposition 2 years ahead
fevd           = compute_variance_decompositions(posterior, horizon = 8)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1, exogenous = us_fiscal_ex) |>
  estimate(S = 5) |> 
  estimate(S = 10) |> 
  compute_variance_decompositions(horizon = 8) -> fevds

# conditional forecasting using a model with exogenous variables
############################################################
data(us_fiscal_ex_forecasts)      # upload exogenous variables future values
data(us_fiscal_cond_forecasts)    # upload a matrix with projected ttr

#' set.seed(123)
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1, exogenous = us_fiscal_ex)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 10)

# forecast 2 years ahead
predictive     = forecast(
                    posterior, 
                    horizon = 8,
                    exogenous_forecast = us_fiscal_ex_forecasts,
                    conditional_forecast = us_fiscal_cond_forecasts
                  )
summary(predictive)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1, exogenous = us_fiscal_ex) |>
  estimate(S = 5) |> 
  estimate(S = 10) |> 
  forecast(
    horizon = 8,
    exogenous_forecast = us_fiscal_ex_forecasts,
    conditional_forecast = us_fiscal_cond_forecasts
  ) |> plot()

Computes posterior draws of structural shock conditional standard deviations

Description

Each of the draws from the posterior estimation of models is transformed into a draw from the posterior distribution of the structural shock conditional standard deviations.

Usage

compute_conditional_sd(posterior)

Arguments

posterior

posterior estimation outcome obtained by running the estimate function. The interpretation depends on the normalisation of the shocks using function normalise_posterior(). Verify if the default settings are appropriate.

Value

An object of class PosteriorSigma, that is, an NxTxS array with attribute PosteriorSigma containing S draws of the structural shock conditional standard deviations.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute structural shocks' conditional standard deviations
sigma          = compute_conditional_sd(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_conditional_sd() -> csd

Computes posterior draws of structural shock conditional standard deviations

Description

Each of the draws from the posterior estimation of models is transformed into a draw from the posterior distribution of the structural shock conditional standard deviations.

Usage

## S3 method for class 'PosteriorBSVAR'
compute_conditional_sd(posterior)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVAR obtained by running the estimate function.

Value

An object of class PosteriorSigma, that is, an NxTxS array with attribute PosteriorSigma containing S draws of the structural shock conditional standard deviations.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute structural shocks' conditional standard deviations
sigma          = compute_conditional_sd(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_conditional_sd() -> csd

Computes posterior draws of structural shock conditional standard deviations

Description

Each of the draws from the posterior estimation of models is transformed into a draw from the posterior distribution of the structural shock conditional standard deviations.

Usage

## S3 method for class 'PosteriorBSVARMIX'
compute_conditional_sd(posterior)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARMIX obtained by running the estimate function.

Value

An object of class PosteriorSigma, that is, an NxTxS array with attribute PosteriorSigma containing S draws of the structural shock conditional standard deviations.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 1, M = 2)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute structural shocks' conditional standard deviations
csd     = compute_conditional_sd(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_mix$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_conditional_sd() -> csd

Computes posterior draws of structural shock conditional standard deviations

Description

Each of the draws from the posterior estimation of models is transformed into a draw from the posterior distribution of the structural shock conditional standard deviations.

Usage

## S3 method for class 'PosteriorBSVARMSH'
compute_conditional_sd(posterior)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARMSH obtained by running the estimate function.

Value

An object of class PosteriorSigma, that is, an NxTxS array with attribute PosteriorSigma containing S draws of the structural shock conditional standard deviations.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 1, M = 2)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute structural shocks' conditional standard deviations
csd     = compute_conditional_sd(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_conditional_sd() -> csd

Computes posterior draws of structural shock conditional standard deviations

Description

Each of the draws from the posterior estimation of models is transformed into a draw from the posterior distribution of the structural shock conditional standard deviations.

Usage

## S3 method for class 'PosteriorBSVARSV'
compute_conditional_sd(posterior)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARSV obtained by running the estimate function.

Value

An object of class PosteriorSigma, that is, an NxTxS array with attribute PosteriorSigma containing S draws of the structural shock conditional standard deviations.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute structural shocks' conditional standard deviations
csd     = compute_conditional_sd(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_conditional_sd() -> csd

Computes posterior draws of structural shock conditional standard deviations

Description

Each of the draws from the posterior estimation of models is transformed into a draw from the posterior distribution of the structural shock conditional standard deviations.

Usage

## S3 method for class 'PosteriorBSVART'
compute_conditional_sd(posterior)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVART obtained by running the estimate function.

Value

An object of class PosteriorSigma, that is, an NxTxS array with attribute PosteriorSigma containing S draws of the structural shock conditional standard deviations.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_t$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute structural shocks' conditional standard deviations
sigma          = compute_conditional_sd(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_t$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_conditional_sd() -> csd

Computes posterior draws from data predictive density

Description

Each of the draws from the posterior estimation of models from packages bsvars or bsvarSIGNs is transformed into a draw from the data predictive density.

Usage

compute_fitted_values(posterior)

Arguments

posterior

posterior estimation outcome obtained by running the estimate function.

Value

An object of class PosteriorFitted, that is, an NxTxS array with attribute PosteriorFitted containing S draws from the data predictive density.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute draws from in-sample predictive density
fitted         = compute_fitted_values(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_fitted_values() -> fitted

Computes posterior draws from data predictive density

Description

Each of the draws from the posterior estimation of models from packages bsvars or bsvarSIGNs is transformed into a draw from the data predictive density.

Usage

## S3 method for class 'PosteriorBSVAR'
compute_fitted_values(posterior)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVAR obtained by running the estimate function.

Value

An object of class PosteriorFitted, that is, an NxTxS array with attribute PosteriorFitted containing S draws from the data predictive density.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute draws from in-sample predictive density
fitted         = compute_fitted_values(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_fitted_values() -> fitted

Computes posterior draws from data predictive density

Description

Each of the draws from the posterior estimation of models from packages bsvars or bsvarSIGNs is transformed into a draw from the data predictive density.

Usage

## S3 method for class 'PosteriorBSVARMIX'
compute_fitted_values(posterior)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARMIX obtained by running the estimate function.

Value

An object of class PosteriorFitted, that is, an NxTxS array with attribute PosteriorFitted containing S draws from the data predictive density.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 1, M = 2)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute draws from in-sample predictive density
csd     = compute_fitted_values(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_mix$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_fitted_values() -> csd

Computes posterior draws from data predictive density

Description

Each of the draws from the posterior estimation of models from packages bsvars or bsvarSIGNs is transformed into a draw from the data predictive density.

Usage

## S3 method for class 'PosteriorBSVARMSH'
compute_fitted_values(posterior)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARMSH obtained by running the estimate function.

Value

An object of class PosteriorFitted, that is, an NxTxS array with attribute PosteriorFitted containing S draws from the data predictive density.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 1, M = 2)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute draws from in-sample predictive density
csd     = compute_fitted_values(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_fitted_values() -> csd

Computes posterior draws from data predictive density

Description

Each of the draws from the posterior estimation of models from packages bsvars or bsvarSIGNs is transformed into a draw from the data predictive density.

Usage

## S3 method for class 'PosteriorBSVARSV'
compute_fitted_values(posterior)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARSV obtained by running the estimate function.

Value

An object of class PosteriorFitted, that is, an NxTxS array with attribute PosteriorFitted containing S draws from the data predictive density.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute draws from in-sample predictive density
csd     = compute_fitted_values(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_fitted_values() -> csd

Computes posterior draws from data predictive density

Description

Each of the draws from the posterior estimation of the model is transformed into a draw from the data predictive density.

Usage

## S3 method for class 'PosteriorBSVART'
compute_fitted_values(posterior)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVART obtained by running the estimate function.

Value

An object of class PosteriorFitted, that is, an NxTxS array with attribute PosteriorFitted containing S draws from the data predictive density.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_t$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute draws from in-sample predictive density
fitted         = compute_fitted_values(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_t$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_fitted_values() -> fitted

Computes posterior draws of historical decompositions

Description

Each of the draws from the posterior estimation of models from packages bsvars or bsvarSIGNs is transformed into a draw from the posterior distribution of the historical decompositions. IMPORTANT! The historical decompositions are interpreted correctly for covariance stationary data. Application to unit-root non-stationary data might result in non-interpretable outcomes.

Usage

compute_historical_decompositions(posterior, show_progress = TRUE)

Arguments

posterior

show_progress

a logical value, if TRUE the estimation progress bar is visible

Value

An object of class PosteriorHD, that is, an NxNxTxS array with attribute PosteriorHD containing S draws of the historical decompositions.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Kilian, L., & Lütkepohl, H. (2017). Structural VAR Tools, Chapter 4, In: Structural vector autoregressive analysis. Cambridge University Press.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(diff(us_fiscal_lsuw), p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute historical decompositions
hd            = compute_historical_decompositions(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
diff(us_fiscal_lsuw) |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_historical_decompositions() -> hd

Computes posterior draws of historical decompositions

Description

Usage

## S3 method for class 'PosteriorBSVAR'
compute_historical_decompositions(posterior, show_progress = TRUE)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVAR obtained by running the estimate function.

show_progress

a logical value, if TRUE the estimation progress bar is visible

Value

An object of class PosteriorHD, that is, an NxNxTxS array with attribute PosteriorHD containing S draws of the historical decompositions.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Kilian, L., & Lütkepohl, H. (2017). Structural VAR Tools, Chapter 4, In: Structural vector autoregressive analysis. Cambridge University Press.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(diff(us_fiscal_lsuw), p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute historical decompositions
hd            = compute_historical_decompositions(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
diff(us_fiscal_lsuw) |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_historical_decompositions() -> hd

Computes posterior draws of historical decompositions

Description

Usage

## S3 method for class 'PosteriorBSVARMIX'
compute_historical_decompositions(posterior, show_progress = TRUE)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARMIX obtained by running the estimate function.

show_progress

a logical value, if TRUE the estimation progress bar is visible

Value

An object of class PosteriorHD, that is, an NxNxTxS array with attribute PosteriorHD containing S draws of the historical decompositions.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Kilian, L., & Lütkepohl, H. (2017). Structural VAR Tools, Chapter 4, In: Structural vector autoregressive analysis. Cambridge University Press.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 1, M = 2)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute historical decompositions
hd             = compute_historical_decompositions(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_mix$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_historical_decompositions() -> hds

Computes posterior draws of historical decompositions

Description

Usage

## S3 method for class 'PosteriorBSVARMSH'
compute_historical_decompositions(posterior, show_progress = TRUE)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARMSH obtained by running the estimate function.

show_progress

a logical value, if TRUE the estimation progress bar is visible

Value

An object of class PosteriorHD, that is, an NxNxTxS array with attribute PosteriorHD containing S draws of the historical decompositions.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Kilian, L., & Lütkepohl, H. (2017). Structural VAR Tools, Chapter 4, In: Structural vector autoregressive analysis. Cambridge University Press.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 1, M = 2)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute historical decompositions
hd             = compute_historical_decompositions(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_historical_decompositions() -> hds

Computes posterior draws of historical decompositions

Description

Usage

## S3 method for class 'PosteriorBSVARSV'
compute_historical_decompositions(posterior, show_progress = TRUE)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARSV obtained by running the estimate function.

show_progress

a logical value, if TRUE the estimation progress bar is visible

Value

An object of class PosteriorHD, that is, an NxNxTxS array with attribute PosteriorHD containing S draws of the historical decompositions.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Kilian, L., & Lütkepohl, H. (2017). Structural VAR Tools, Chapter 4, In: Structural vector autoregressive analysis. Cambridge University Press.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 5)

# estimate the model
posterior      = estimate(burn_in, 5)

# compute historical decompositions
hd             = compute_historical_decompositions(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  compute_historical_decompositions() -> hds

Computes posterior draws of historical decompositions

Description

Usage

## S3 method for class 'PosteriorBSVART'
compute_historical_decompositions(posterior, show_progress = TRUE)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVART obtained by running the estimate function.

show_progress

a logical value, if TRUE the estimation progress bar is visible

Value

An object of class PosteriorHD, that is, an NxNxTxS array with attribute PosteriorHD containing S draws of the historical decompositions.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Kilian, L., & Lütkepohl, H. (2017). Structural VAR Tools, Chapter 4, In: Structural vector autoregressive analysis. Cambridge University Press.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_t$new(diff(us_fiscal_lsuw), p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 10)

# compute historical decompositions
hd            = compute_historical_decompositions(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
diff(us_fiscal_lsuw) |>
  specify_bsvar_t$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 10) |> 
  compute_historical_decompositions() -> hd

Computes posterior draws of impulse responses

Description

Each of the draws from the posterior estimation of models from packages bsvars or bsvarSIGNs is transformed into a draw from the posterior distribution of the impulse responses.

Usage

compute_impulse_responses(posterior, horizon, standardise = FALSE)

Arguments

posterior

horizon

a positive integer number denoting the forecast horizon for the impulse responses computations.

standardise

a logical value. If TRUE, the impulse responses are standardised so that the variables' own shocks at horizon 0 are equal to 1. Otherwise, the parameter estimates determine this magnitude.

Value

An object of class PosteriorIR, that is, an NxNx(horizon+1)xS array with attribute PosteriorIR containing S draws of the impulse responses.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Kilian, L., & Lütkepohl, H. (2017). Structural VAR Tools, Chapter 4, In: Structural vector autoregressive analysis. Cambridge University Press.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute impulse responses 2 years ahead
irf           = compute_impulse_responses(posterior, horizon = 8)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_impulse_responses(horizon = 8) -> ir

Computes posterior draws of impulse responses

Description

Each of the draws from the posterior estimation of models from packages bsvars or bsvarSIGNs is transformed into a draw from the posterior distribution of the impulse responses.

Usage

## S3 method for class 'PosteriorBSVAR'
compute_impulse_responses(posterior, horizon, standardise = FALSE)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVAR obtained by running the estimate function.

horizon

a positive integer number denoting the forecast horizon for the impulse responses computations.

standardise

a logical value. If TRUE, the impulse responses are standardised so that the variables' own shocks at horizon 0 are equal to 1. Otherwise, the parameter estimates determine this magnitude.

Value

An object of class PosteriorIR, that is, an NxNx(horizon+1)xS array with attribute PosteriorIR containing S draws of the impulse responses.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Kilian, L., & Lütkepohl, H. (2017). Structural VAR Tools, Chapter 4, In: Structural vector autoregressive analysis. Cambridge University Press.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute impulse responses 2 years ahead
irf           = compute_impulse_responses(posterior, horizon = 8)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_impulse_responses(horizon = 8) -> ir

Computes posterior draws of impulse responses

Description

Each of the draws from the posterior estimation of models from packages bsvars or bsvarSIGNs is transformed into a draw from the posterior distribution of the impulse responses.

Usage

## S3 method for class 'PosteriorBSVARMIX'
compute_impulse_responses(posterior, horizon, standardise = FALSE)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARMIX obtained by running the estimate function.

horizon

a positive integer number denoting the forecast horizon for the impulse responses computations.

standardise

a logical value. If TRUE, the impulse responses are standardised so that the variables' own shocks at horizon 0 are equal to 1. Otherwise, the parameter estimates determine this magnitude.

Value

An object of class PosteriorIR, that is, an NxNx(horizon+1)xS array with attribute PosteriorIR containing S draws of the impulse responses.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Kilian, L., & Lütkepohl, H. (2017). Structural VAR Tools, Chapter 4, In: Structural vector autoregressive analysis. Cambridge University Press.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 1, M = 2)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute impulse responses
irfs            = compute_impulse_responses(posterior, 4)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_mix$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_impulse_responses(horizon = 4) -> irfs

Computes posterior draws of impulse responses

Description

Each of the draws from the posterior estimation of models from packages bsvars or bsvarSIGNs is transformed into a draw from the posterior distribution of the impulse responses.

Usage

## S3 method for class 'PosteriorBSVARMSH'
compute_impulse_responses(posterior, horizon, standardise = FALSE)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARMSH obtained by running the estimate function.

horizon

a positive integer number denoting the forecast horizon for the impulse responses computations.

standardise

a logical value. If TRUE, the impulse responses are standardised so that the variables' own shocks at horizon 0 are equal to 1. Otherwise, the parameter estimates determine this magnitude.

Value

An object of class PosteriorIR, that is, an NxNx(horizon+1)xS array with attribute PosteriorIR containing S draws of the impulse responses.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Kilian, L., & Lütkepohl, H. (2017). Structural VAR Tools, Chapter 4, In: Structural vector autoregressive analysis. Cambridge University Press.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 1, M = 2)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute impulse responses
irfs            = compute_impulse_responses(posterior, 4)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_impulse_responses(horizon = 4) -> irfs

Computes posterior draws of impulse responses

Description

Each of the draws from the posterior estimation of models from packages bsvars or bsvarSIGNs is transformed into a draw from the posterior distribution of the impulse responses.

Usage

## S3 method for class 'PosteriorBSVARSV'
compute_impulse_responses(posterior, horizon, standardise = FALSE)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARSV obtained by running the estimate function.

horizon

a positive integer number denoting the forecast horizon for the impulse responses computations.

standardise

a logical value. If TRUE, the impulse responses are standardised so that the variables' own shocks at horizon 0 are equal to 1. Otherwise, the parameter estimates determine this magnitude.

Value

An object of class PosteriorIR, that is, an NxNx(horizon+1)xS array with attribute PosteriorIR containing S draws of the impulse responses.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Kilian, L., & Lütkepohl, H. (2017). Structural VAR Tools, Chapter 4, In: Structural vector autoregressive analysis. Cambridge University Press.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute impulse responses
irfs            = compute_impulse_responses(posterior, 4)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_impulse_responses(horizon = 4) -> irfs

Computes posterior draws of impulse responses

Description

Each of the draws from the posterior estimation of models from packages bsvars or bsvarSIGNs is transformed into a draw from the posterior distribution of the impulse responses.

Usage

## S3 method for class 'PosteriorBSVART'
compute_impulse_responses(posterior, horizon, standardise = FALSE)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVART obtained by running the estimate function.

horizon

a positive integer number denoting the forecast horizon for the impulse responses computations.

standardise

a logical value. If TRUE, the impulse responses are standardised so that the variables' own shocks at horizon 0 are equal to 1. Otherwise, the parameter estimates determine this magnitude.

Value

An object of class PosteriorIR, that is, an NxNx(horizon+1)xS array with attribute PosteriorIR containing S draws of the impulse responses.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Kilian, L., & Lütkepohl, H. (2017). Structural VAR Tools, Chapter 4, In: Structural vector autoregressive analysis. Cambridge University Press.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_t$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute impulse responses
irfs            = compute_impulse_responses(posterior, 4)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_t$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_impulse_responses(horizon = 4) -> irfs

Computes posterior draws of regime probabilities

Description

Each of the draws from the posterior estimation of a model is transformed into a draw from the posterior distribution of the regime probabilities. These represent either the realisations of the regime indicators, when type = "realized", filtered probabilities, when type = "filtered", forecasted regime probabilities, when type = "forecasted", or the smoothed probabilities, when type = "smoothed", .

Usage

compute_regime_probabilities(
  posterior,
  type = c("realized", "filtered", "forecasted", "smoothed")
)

Arguments

posterior

posterior estimation outcome of regime-dependent heteroskedastic models - an object of either of the classes: PosteriorBSVARMSH, or PosteriorBSVARMIX obtained by running the estimate function.

type

one of the values "realized", "filtered", "forecasted", or "smoothed" denoting the type of probabilities to be computed.

Value

An object of class PosteriorRegimePr, that is, an MxTxS array with attribute PosteriorRegimePr containing S draws of the regime probabilities.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Song, Y., and Woźniak, T., (2021) Markov Switching. Oxford Research Encyclopedia of Economics and Finance, Oxford University Press, doi:10.1093/acrefore/9780190625979.013.174.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 2, M = 2)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute the posterior draws of realized regime indicators
regimes        = compute_regime_probabilities(posterior)

# compute the posterior draws of filtered probabilities
filtered       = compute_regime_probabilities(posterior, "filtered")

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  estimate(S = 20) -> posterior
regimes        = compute_regime_probabilities(posterior)
filtered       = compute_regime_probabilities(posterior, "filtered")

Computes posterior draws of regime probabilities

Description

Usage

## S3 method for class 'PosteriorBSVARMIX'
compute_regime_probabilities(
  posterior,
  type = c("realized", "filtered", "forecasted", "smoothed")
)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARMIX obtained by running the estimate function.

type

one of the values "realized", "filtered", "forecasted", or "smoothed" denoting the type of probabilities to be computed.

Value

An object of class PosteriorRegimePr, that is, an MxTxS array with attribute PosteriorRegimePr containing S draws of the regime probabilities.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Song, Y., and Woźniak, T., (2021) Markov Switching. Oxford Research Encyclopedia of Economics and Finance, Oxford University Press, doi:10.1093/acrefore/9780190625979.013.174.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 2, M = 2)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute the posterior draws of realized regime indicators
regimes        = compute_regime_probabilities(posterior)

# compute the posterior draws of filtered probabilities
filtered       = compute_regime_probabilities(posterior, "filtered")

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_mix$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  estimate(S = 20) -> posterior
regimes        = compute_regime_probabilities(posterior)
filtered       = compute_regime_probabilities(posterior, "filtered")

Computes posterior draws of regime probabilities

Description

Usage

## S3 method for class 'PosteriorBSVARMSH'
compute_regime_probabilities(
  posterior,
  type = c("realized", "filtered", "forecasted", "smoothed")
)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARMSH obtained by running the estimate function.

type

one of the values "realized", "filtered", "forecasted", or "smoothed" denoting the type of probabilities to be computed.

Value

An object of class PosteriorRegimePr, that is, an MxTxS array with attribute PosteriorRegimePr containing S draws of the regime probabilities.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Song, Y., and Woźniak, T., (2021) Markov Switching. Oxford Research Encyclopedia of Economics and Finance, Oxford University Press, doi:10.1093/acrefore/9780190625979.013.174.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 2, M = 2)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute the posterior draws of realized regime indicators
regimes        = compute_regime_probabilities(posterior)

# compute the posterior draws of filtered probabilities
filtered       = compute_regime_probabilities(posterior, "filtered")

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  estimate(S = 20) -> posterior
regimes        = compute_regime_probabilities(posterior)
filtered       = compute_regime_probabilities(posterior, "filtered")

Computes posterior draws of structural shocks

Description

Each of the draws from the posterior estimation of models from packages bsvars or bsvarSIGNs is transformed into a draw from the posterior distribution of the structural shocks.

Usage

compute_structural_shocks(posterior)

Arguments

posterior

Value

An object of class PosteriorShocks, that is, an NxTxS array with attribute PosteriorShocks containing S draws of the structural shocks.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute structural shocks
shocks         = compute_structural_shocks(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_structural_shocks() -> ss

Computes posterior draws of structural shocks

Description

Each of the draws from the posterior estimation of models from packages bsvars or bsvarSIGNs is transformed into a draw from the posterior distribution of the structural shocks.

Usage

## S3 method for class 'PosteriorBSVAR'
compute_structural_shocks(posterior)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVAR obtained by running the estimate function.

Value

An object of class PosteriorShocks, that is, an NxTxS array with attribute PosteriorShocks containing S draws of the structural shocks.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute structural shocks
shocks         = compute_structural_shocks(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_structural_shocks() -> ss

Computes posterior draws of structural shocks

Description

Each of the draws from the posterior estimation of models from packages bsvars or bsvarSIGNs is transformed into a draw from the posterior distribution of the structural shocks.

Usage

## S3 method for class 'PosteriorBSVARMIX'
compute_structural_shocks(posterior)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARMIX obtained by running the estimate function.

Value

An object of class PosteriorShocks, that is, an NxTxS array with attribute PosteriorShocks containing S draws of the structural shocks.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 1, M = 2)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute structural shocks
shocks         = compute_structural_shocks(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_mix$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_structural_shocks() -> ss

Computes posterior draws of structural shocks

Description

Each of the draws from the posterior estimation of models from packages bsvars or bsvarSIGNs is transformed into a draw from the posterior distribution of the structural shocks.

Usage

## S3 method for class 'PosteriorBSVARMSH'
compute_structural_shocks(posterior)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARMSH obtained by running the estimate function.

Value

An object of class PosteriorShocks, that is, an NxTxS array with attribute PosteriorShocks containing S draws of the structural shocks.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 1, M = 2)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute structural shocks
shocks         = compute_structural_shocks(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_structural_shocks() -> ss

Computes posterior draws of structural shocks

Description

Each of the draws from the posterior estimation of models from packages bsvars or bsvarSIGNs is transformed into a draw from the posterior distribution of the structural shocks.

Usage

## S3 method for class 'PosteriorBSVARSV'
compute_structural_shocks(posterior)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARSV obtained by running the estimate function.

Value

An object of class PosteriorShocks, that is, an NxTxS array with attribute PosteriorShocks containing S draws of the structural shocks.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute structural shocks
shocks         = compute_structural_shocks(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_structural_shocks() -> ss

Computes posterior draws of structural shocks

Description

Each of the draws from the posterior estimation of models from packages bsvars or bsvarSIGNs is transformed into a draw from the posterior distribution of the structural shocks.

Usage

## S3 method for class 'PosteriorBSVART'
compute_structural_shocks(posterior)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVART obtained by running the estimate function.

Value

An object of class PosteriorShocks, that is, an NxTxS array with attribute PosteriorShocks containing S draws of the structural shocks.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_t$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute structural shocks
shocks         = compute_structural_shocks(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_t$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_structural_shocks() -> ss

Computes posterior draws of the forecast error variance decomposition

Description

Each of the draws from the posterior estimation of models from packages bsvars or bsvarSIGNs is transformed into a draw from the posterior distribution of the forecast error variance decomposition.

Usage

compute_variance_decompositions(posterior, horizon)

Arguments

posterior

horizon

a positive integer number denoting the forecast horizon for the forecast error variance decomposition computations.

Value

An object of class PosteriorFEVD, that is, an NxNx(horizon+1)xS array with attribute PosteriorFEVD containing S draws of the forecast error variance decomposition.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Kilian, L., & Lütkepohl, H. (2017). Structural VAR Tools, Chapter 4, In: Structural vector autoregressive analysis. Cambridge University Press.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute forecast error variance decomposition 2 years ahead
fevd           = compute_variance_decompositions(posterior, horizon = 8)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_variance_decompositions(horizon = 8) -> fevd

Computes posterior draws of the forecast error variance decomposition

Description

Each of the draws from the posterior estimation of the model is transformed into a draw from the posterior distribution of the forecast error variance decomposition.

Usage

## S3 method for class 'PosteriorBSVAR'
compute_variance_decompositions(posterior, horizon)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVAR obtained by running the estimate function.

horizon

a positive integer number denoting the forecast horizon for the forecast error variance decomposition computations.

Value

An object of class PosteriorFEVD, that is, an NxNx(horizon+1)xS array with attribute PosteriorFEVD containing S draws of the forecast error variance decomposition.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Kilian, L., & Lütkepohl, H. (2017). Structural VAR Tools, Chapter 4, In: Structural vector autoregressive analysis. Cambridge University Press.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute forecast error variance decomposition 2 years ahead
fevd           = compute_variance_decompositions(posterior, horizon = 8)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_variance_decompositions(horizon = 8) -> fevd

Computes posterior draws of the forecast error variance decomposition

Description

Each of the draws from the posterior estimation of the model is transformed into a draw from the posterior distribution of the forecast error variance decomposition. In this mixture model the forecast error variance decompositions are computed for the forecasts with the origin at the last observation in sample data and using the conditional variance forecasts.

Usage

## S3 method for class 'PosteriorBSVARMIX'
compute_variance_decompositions(posterior, horizon)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARMIX obtained by running the estimate function.

horizon

a positive integer number denoting the forecast horizon for the forecast error variance decomposition computations.

Value

An object of class PosteriorFEVD, that is, an NxNx(horizon+1)xS array with attribute PosteriorFEVD containing S draws of the forecast error variance decomposition.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Kilian, L., & Lütkepohl, H. (2017). Structural VAR Tools, Chapter 4, In: Structural vector autoregressive analysis. Cambridge University Press.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 1, M = 2)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute forecast error variance decomposition 2 years ahead
fevd           = compute_variance_decompositions(posterior, horizon = 8)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_mix$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_variance_decompositions(horizon = 8) -> fevd

Computes posterior draws of the forecast error variance decomposition

Description

Each of the draws from the posterior estimation of the model is transformed into a draw from the posterior distribution of the forecast error variance decomposition. In this heteroskedastic model the forecast error variance decompositions are computed for the forecasts with the origin at the last observation in sample data and using the conditional variance forecasts.

Usage

## S3 method for class 'PosteriorBSVARMSH'
compute_variance_decompositions(posterior, horizon)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARMSH obtained by running the estimate function.

horizon

a positive integer number denoting the forecast horizon for the forecast error variance decomposition computations.

Value

An object of class PosteriorFEVD, that is, an NxNx(horizon+1)xS array with attribute PosteriorFEVD containing S draws of the forecast error variance decomposition.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Kilian, L., & Lütkepohl, H. (2017). Structural VAR Tools, Chapter 4, In: Structural vector autoregressive analysis. Cambridge University Press.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 1, M = 2)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute forecast error variance decomposition 2 years ahead
fevd           = compute_variance_decompositions(posterior, horizon = 8)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_variance_decompositions(horizon = 8) -> fevd

Computes posterior draws of the forecast error variance decomposition

Description

Usage

## S3 method for class 'PosteriorBSVARSV'
compute_variance_decompositions(posterior, horizon)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARSV obtained by running the estimate function.

horizon

a positive integer number denoting the forecast horizon for the forecast error variance decomposition computations.

Value

An object of class PosteriorFEVD, that is, an NxNx(horizon+1)xS array with attribute PosteriorFEVD containing S draws of the forecast error variance decomposition.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Kilian, L., & Lütkepohl, H. (2017). Structural VAR Tools, Chapter 4, In: Structural vector autoregressive analysis. Cambridge University Press.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute forecast error variance decomposition 2 years ahead
fevd           = compute_variance_decompositions(posterior, horizon = 8)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_variance_decompositions(horizon = 8) -> fevd

Computes posterior draws of the forecast error variance decomposition

Description

Each of the draws from the posterior estimation of the model is transformed into a draw from the posterior distribution of the forecast error variance decomposition.

Usage

## S3 method for class 'PosteriorBSVART'
compute_variance_decompositions(posterior, horizon)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVART obtained by running the estimate function.

horizon

a positive integer number denoting the forecast horizon for the forecast error variance decomposition computations.

Value

An object of class PosteriorFEVD, that is, an NxNx(horizon+1)xS array with attribute PosteriorFEVD containing S draws of the forecast error variance decomposition.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Kilian, L., & Lütkepohl, H. (2017). Structural VAR Tools, Chapter 4, In: Structural vector autoregressive analysis. Cambridge University Press.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_t$new(us_fiscal_lsuw)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute forecast error variance decomposition 2 years ahead
fevd           = compute_variance_decompositions(posterior, horizon = 8)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_t$new() |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_variance_decompositions(horizon = 8) -> fevd

Bayesian estimation of Structural Vector Autoregressions via Gibbs sampler

Description

Estimates homo- or heteroskedastic SVAR models for packages bsvars and bsvarSIGNs. The packages apply the Gibbs sampler proposed by Waggoner & Zha (2003) for the structural matrix B and the equation-by-equation sampler by Chan, Koop, & Yu (2024) for the autoregressive slope parameters A. Additionally, the parameter matrices A and B follow a Minnesota prior and generalised-normal prior distributions respectively with the matrix-specific 3-level equation-specific local-global hierarchical prior for the shrinkage parameters. A variety of models for conditional variances are possible including versions of Stochastic Volatility and Markov-switching heteroskedasticity. Non-normal specifications include finite and sparse normal mixture model for the structural shocks. The estimation algorithms for particular models are scrutinised in Lütkepohl, Shang, Uzeda, & Woźniak (2024) and Woźniak & Droumaguet (2024) and some other inferential and identification problems are considered in Lütkepohl & Woźniak (2020) and Song & Woźniak (2021). Models from package bsvars implement identification via exclusion restrictions, heteroskedasticity and non-normality. Models from package bsvarSIGNs implement identification via sign and narrative restrictions. See section Details and package bsvarSIGNs documentation for more information.

Usage

estimate(specification, S, thin = 1, show_progress = TRUE)

Arguments

specification

an object generated using one of the specify_bsvar* functions or an object generated using the function estimate. The latter type of input facilitates the continuation of the MCMC sampling starting from the last draw of the previous run.

S

a positive integer, the number of posterior draws to be generated

thin

a positive integer, specifying the frequency of MCMC output thinning

show_progress

a logical value, if TRUE the estimation progress bar is visible

Details

The homoskedastic SVAR model is given by the reduced form equation:

Y = AX + E

The structural equation is given by

BE = U

where U is an NxT matrix of structural form error terms, and B is an NxN matrix of contemporaneous relationships.

The structural shocks, U, are temporally and contemporaneously independent and jointly normally distributed with zero mean and unit variances.

The various SVAR models estimated differ by the specification of structural shocks variances. Their specification depends on the specify_bsvar* function used. The different models include:

homoskedastic model with unit variances
heteroskedastic model with stationary Markov switching in the variances
heteroskedastic model with Stochastic Volatility process for variances
non-normal model with a finite mixture of normal components and component-specific variances
heteroskedastic model with sparse Markov switching in the variances where the number of heteroskedastic components is estimated
non-normal model with a sparse mixture of normal components and component-specific variances where the number of heteroskedastic components is estimated

Value

An object of class PosteriorBSVAR* containing the Bayesian estimation output and containing two elements:

posterior a list with a collection of S draws from the posterior distribution generated via Gibbs sampler containing many arrays and vectors whose selection depends on the model specification. last_draw an object generated by one of the specify_bsvar* functions with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Chan, J.C.C., Koop, G, and Yu, X. (2024) Large Order-Invariant Bayesian VARs with Stochastic Volatility. Journal of Business & Economic Statistics, 42, doi:10.1080/07350015.2023.2252039.

Waggoner, D.F., and Zha, T., (2003) A Gibbs sampler for structural vector autoregressions. Journal of Economic Dynamics and Control, 28, 349–366, doi:10.1016/S0165-1889(02)00168-9.

Woźniak, T., and Droumaguet, M., (2024) Bayesian Assessment of Identifying Restrictions for Heteroskedastic Structural VARs.

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 4)
set.seed(123)

# run the burn-in
burn_in        = estimate(specification, 5)

# estimate the model
posterior      = estimate(burn_in, 10, thin = 2)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 10, thin = 2) -> posterior

Bayesian estimation of a homoskedastic Structural Vector Autoregression via Gibbs sampler

Description

Estimates the homoskedastic SVAR using the Gibbs sampler proposed by Waggoner & Zha (2003) for the structural matrix B and the equation-by-equation sampler by Chan, Koop, & Yu (2024) for the autoregressive slope parameters A. Additionally, the parameter matrices A and B follow a Minnesota prior and generalised-normal prior distributions respectively with the matrix-specific overall shrinkage parameters estimated using a hierarchical prior distribution as in Lütkepohl, Shang, Uzeda, and Woźniak (2024). See section Details for the model equations.

Usage

## S3 method for class 'BSVAR'
estimate(specification, S, thin = 1, show_progress = TRUE)

Arguments

specification

an object of class BSVAR generated using the specify_bsvar$new() function.

S

a positive integer, the number of posterior draws to be generated

thin

a positive integer, specifying the frequency of MCMC output thinning

show_progress

a logical value, if TRUE the estimation progress bar is visible

Details

The homoskedastic SVAR model is given by the reduced form equation:

Y = AX + E

The structural equation is given by

BE = U

where U is an NxT matrix of structural form error terms, and B is an NxN matrix of contemporaneous relationships.

Finally, the structural shocks, U, are temporally and contemporaneously independent and jointly normally distributed with zero mean and unit variances.

Value

An object of class PosteriorBSVAR containing the Bayesian estimation output and containing two elements:

posterior a list with a collection of S draws from the posterior distribution generated via Gibbs sampler containing:

A: an NxKxS array with the posterior draws for matrix A
B: an NxNxS array with the posterior draws for matrix B
hyper: a 5xS matrix with the posterior draws for the hyper-parameters of the hierarchical prior distribution

last_draw an object of class BSVAR with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Chan, J.C.C., Koop, G, and Yu, X. (2024) Large Order-Invariant Bayesian VARs with Stochastic Volatility. Journal of Business & Economic Statistics, 42, doi:10.1080/07350015.2023.2252039.

Waggoner, D.F., and Zha, T., (2003) A Gibbs sampler for structural vector autoregressions. Journal of Economic Dynamics and Control, 28, 349–366, doi:10.1016/S0165-1889(02)00168-9.

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 4)
set.seed(123)

# run the burn-in
burn_in        = estimate(specification, 5)

# estimate the model
posterior      = estimate(burn_in, 10, thin = 2)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 10, thin = 2) |> 
  compute_impulse_responses(horizon = 4) -> irf

Bayesian estimation of a Structural Vector Autoregression with shocks following a finite mixture of normal components via Gibbs sampler

Description

Estimates the SVAR with non-normal residuals following a finite M mixture of normal distributions proposed by Woźniak & Droumaguet (2022). Implements the Gibbs sampler proposed by Waggoner & Zha (2003) for the structural matrix B and the equation-by-equation sampler by Chan, Koop, & Yu (2024) for the autoregressive slope parameters A. Additionally, the parameter matrices A and B follow a Minnesota prior and generalised-normal prior distributions respectively with the matrix-specific overall shrinkage parameters estimated thanks to a hierarchical prior distribution. The finite mixture of normals model is estimated using the prior distributions and algorithms proposed by Woźniak & Droumaguet (2024), Lütkepohl & Woźniak (2020), and Song & Woźniak (2021). See section Details for the model equations.

Usage

## S3 method for class 'BSVARMIX'
estimate(specification, S, thin = 1, show_progress = TRUE)

Arguments

specification

an object of class BSVARMIX generated using the specify_bsvar_mix$new() function.

S

a positive integer, the number of posterior draws to be generated

thin

a positive integer, specifying the frequency of MCMC output thinning

show_progress

a logical value, if TRUE the estimation progress bar is visible

Details

The heteroskedastic SVAR model is given by the reduced form equation:

Y = AX + E

The structural equation is given by

BE = U

where U is an NxT matrix of structural form error terms, and B is an NxN matrix of contemporaneous relationships.

Finally, the structural shocks, U, are temporally and contemporaneously independent and finite-mixture of normals distributed with zero mean. The conditional variance of the nth shock at time t is given by:

Var_{t-1}[u_{n.t}] = s^2_{n.s_t}

where s_t is a the regime indicator of the regime-specific conditional variances of structural shocks s^2_{n.s_t}. In this model, the variances of each of the structural shocks sum to M.

The regime indicator s_t is either such that:

the regime probabilities are non-zero which requires all regimes to have a positive number occurrences over the sample period, or
sparse with potentially many regimes with zero occurrences over the sample period and in which the number of regimes is estimated.

These model selection also with this respect is made using function specify_bsvar_mix.

Value

An object of class PosteriorBSVARMIX containing the Bayesian estimation output and containing two elements:

posterior a list with a collection of S draws from the posterior distribution generated via Gibbs sampler containing:

A: an NxKxS array with the posterior draws for matrix A
B: an NxNxS array with the posterior draws for matrix B
hyper: a 5xS matrix with the posterior draws for the hyper-parameters of the hierarchical prior distribution
sigma2: an NxMxS array with the posterior draws for the structural shocks conditional variances
PR_TR: an MxMxS array with the posterior draws for the transition matrix.
xi: an MxTxS array with the posterior draws for the regime allocation matrix.
pi_0: an MxS matrix with the posterior draws for the ergodic probabilities
sigma: an NxTxS array with the posterior draws for the structural shocks conditional standard deviations' series over the sample period

last_draw an object of class BSVARMIX with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Chan, J.C.C., Koop, G, and Yu, X. (2024) Large Order-Invariant Bayesian VARs with Stochastic Volatility. Journal of Business & Economic Statistics, 42, doi:10.1080/07350015.2023.2252039.

Song, Y., and Woźniak, T., (2021) Markov Switching. Oxford Research Encyclopedia of Economics and Finance, Oxford University Press, doi:10.1093/acrefore/9780190625979.013.174.

Waggoner, D.F., and Zha, T., (2003) A Gibbs sampler for structural vector autoregressions. Journal of Economic Dynamics and Control, 28, 349–366, doi:10.1016/S0165-1889(02)00168-9.

Woźniak, T., and Droumaguet, M., (2024) Bayesian Assessment of Identifying Restrictions for Heteroskedastic Structural VARs

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 1, M = 2)
set.seed(123)

# run the burn-in
burn_in        = estimate(specification, 5)

# estimate the model
posterior      = estimate(burn_in, 10, thin = 2)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_mix$new(p = 1, M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 10, thin = 2) |> 
  compute_impulse_responses(horizon = 4) -> irf

Bayesian estimation of a Structural Vector Autoregression with Markov-switching heteroskedasticity via Gibbs sampler

Description

Estimates the SVAR with Markov-switching heteroskedasticity with M regimes (MS(M)) proposed by Woźniak & Droumaguet (2022). Implements the Gibbs sampler proposed by Waggoner & Zha (2003) for the structural matrix B and the equation-by-equation sampler by Chan, Koop, & Yu (2024) for the autoregressive slope parameters A. Additionally, the parameter matrices A and B follow a Minnesota prior and generalised-normal prior distributions respectively with the matrix-specific overall shrinkage parameters estimated thanks to a hierarchical prior distribution. The MS model is estimated using the prior distributions and algorithms proposed by Woźniak & Droumaguet (2024), Lütkepohl & Woźniak (2020), and Song & Woźniak (2021). See section Details for the model equations.

Usage

## S3 method for class 'BSVARMSH'
estimate(specification, S, thin = 1, show_progress = TRUE)

Arguments

specification

an object of class BSVARMSH generated using the specify_bsvar_msh$new() function.

S

a positive integer, the number of posterior draws to be generated

thin

a positive integer, specifying the frequency of MCMC output thinning

show_progress

a logical value, if TRUE the estimation progress bar is visible

Details

The heteroskedastic SVAR model is given by the reduced form equation:

Y = AX + E

The structural equation is given by

BE = U

where U is an NxT matrix of structural form error terms, and B is an NxN matrix of contemporaneous relationships.

Finally, the structural shocks, U, are temporally and contemporaneously independent and jointly normally distributed with zero mean. The conditional variance of the nth shock at time t is given by:

Var_{t-1}[u_{n.t}] = s^2_{n.s_t}

where s_t is a Markov process driving the time-variability of the regime-specific conditional variances of structural shocks s^2_{n.s_t}. In this model, the variances of each of the structural shocks sum to M.

The Markov process s_t is either:

stationary, irreducible, and aperiodic which requires all regimes to have a positive number occurrences over the sample period, or
sparse with potentially many regimes with zero occurrences over the sample period and in which the number of regimes is estimated.

These model selection also with this respect is made using function specify_bsvar_msh.

Value

An object of class PosteriorBSVARMSH containing the Bayesian estimation output and containing two elements:

posterior a list with a collection of S draws from the posterior distribution generated via Gibbs sampler containing:

A: an NxKxS array with the posterior draws for matrix A
B: an NxNxS array with the posterior draws for matrix B
hyper: a 5xS matrix with the posterior draws for the hyper-parameters of the hierarchical prior distribution
sigma2: an NxMxS array with the posterior draws for the structural shocks conditional variances
PR_TR: an MxMxS array with the posterior draws for the transition matrix.
xi: an MxTxS array with the posterior draws for the regime allocation matrix.
pi_0: an MxS matrix with the posterior draws for the initial state probabilities
sigma: an NxTxS array with the posterior draws for the structural shocks conditional standard deviations' series over the sample period

last_draw an object of class BSVARMSH with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Chan, J.C.C., Koop, G, and Yu, X. (2024) Large Order-Invariant Bayesian VARs with Stochastic Volatility. Journal of Business & Economic Statistics, 42, doi:10.1080/07350015.2023.2252039.

Song, Y., and Woźniak, T., (2021) Markov Switching. Oxford Research Encyclopedia of Economics and Finance, Oxford University Press, doi:10.1093/acrefore/9780190625979.013.174.

Waggoner, D.F., and Zha, T., (2003) A Gibbs sampler for structural vector autoregressions. Journal of Economic Dynamics and Control, 28, 349–366, doi:10.1016/S0165-1889(02)00168-9.

Woźniak, T., and Droumaguet, M., (2024) Bayesian Assessment of Identifying Restrictions for Heteroskedastic Structural VARs

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 1, M = 2)
set.seed(123)

# run the burn-in
burn_in        = estimate(specification, 5)

# estimate the model
posterior      = estimate(burn_in, 10, thin = 2)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new(p = 1, M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 10, thin = 2) |> 
  compute_impulse_responses(horizon = 4) -> irf

Bayesian estimation of a Structural Vector Autoregression with Stochastic Volatility heteroskedasticity via Gibbs sampler

Description

Estimates the SVAR with Stochastic Volatility (SV) heteroskedasticity proposed by Lütkepohl, Shang, Uzeda, and Woźniak (2024). Implements the Gibbs sampler proposed by Waggoner & Zha (2003) for the structural matrix B and the equation-by-equation sampler by Chan, Koop, & Yu (2024) for the autoregressive slope parameters A. Additionally, the parameter matrices A and B follow a Minnesota prior and generalised-normal prior distributions respectively with the matrix-specific overall shrinkage parameters estimated thanks to a hierarchical prior distribution. The SV model is estimated using a range of techniques including: simulation smoother, auxiliary mixture, ancillarity-sufficiency interweaving strategy, and generalised inverse Gaussian distribution summarised by Kastner & Frühwirth-Schnatter (2014). See section Details for the model equations.

Usage

## S3 method for class 'BSVARSV'
estimate(specification, S, thin = 1, show_progress = TRUE)

Arguments

specification

an object of class BSVARSV generated using the specify_bsvar_sv$new() function.

S

a positive integer, the number of posterior draws to be generated

thin

a positive integer, specifying the frequency of MCMC output thinning

show_progress

a logical value, if TRUE the estimation progress bar is visible

Details

The heteroskedastic SVAR model is given by the reduced form equation:

Y = AX + E

The structural equation is given by

BE = U

where U is an NxT matrix of structural form error terms, and B is an NxN matrix of contemporaneous relationships. Finally, the structural shocks, U, are temporally and contemporaneously independent and jointly normally distributed with zero mean.

Two alternative specifications of the conditional variance of the nth shock at time t can be estimated: non-centred Stochastic Volatility by Lütkepohl, Shang, Uzeda, and Woźniak (2022) or centred Stochastic Volatility by Chan, Koop, & Yu (2021).

The non-centred Stochastic Volatility by Lütkepohl, Shang, Uzeda, and Woźniak (2022) is selected by setting argument centred_sv of function specify_bsvar_sv$new() to value FALSE. It has the conditional variances given by:

Var_{t-1}[u_{n.t}] = exp(w_n h_{n.t})

where w_n is the estimated conditional standard deviation of the log-conditional variance and the log-volatility process h_{n.t} follows an autoregressive process:

h_{n.t} = g_n h_{n.t-1} + v_{n.t}

where h_{n.0}=0, g_n is an autoregressive parameter and v_{n.t} is a standard normal error term.

The centred Stochastic Volatility by Chan, Koop, & Yu (2021) is selected by setting argument centred_sv of function specify_bsvar_sv$new() to value TRUE. Its conditional variances are given by:

Var_{t-1}[u_{n.t}] = exp(h_{n.t})

where the log-conditional variances h_{n.t} follow an autoregressive process:

h_{n.t} = g_n h_{n.t-1} + v_{n.t}

where h_{n.0}=0, g_n is an autoregressive parameter and v_{n.t} is a zero-mean normal error term with variance s_{v.n}^2.

Value

An object of class PosteriorBSVARSV containing the Bayesian estimation output and containing two elements:

posterior a list with a collection of S draws from the posterior distribution generated via Gibbs sampler containing:

A: an NxKxS array with the posterior draws for matrix A
B: an NxNxS array with the posterior draws for matrix B
hyper: a 5xS matrix with the posterior draws for the hyper-parameters of the hierarchical prior distribution
h: an NxTxS array with the posterior draws of the log-volatility processes
rho: an NxS matrix with the posterior draws of SV autoregressive parameters
omega: an NxS matrix with the posterior draws of SV process conditional standard deviations
S: an NxTxS array with the posterior draws of the auxiliary mixture component indicators
sigma2_omega: an NxS matrix with the posterior draws of the variances of the zero-mean normal prior for omega
s_: an S-vector with the posterior draws of the scale of the gamma prior of the hierarchical prior for sigma2_omega

last_draw an object of class BSVARSV with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Chan, J.C.C., Koop, G, and Yu, X. (2024) Large Order-Invariant Bayesian VARs with Stochastic Volatility. Journal of Business & Economic Statistics, 42, doi:10.1080/07350015.2023.2252039.

Waggoner, D.F., and Zha, T., (2003) A Gibbs sampler for structural vector autoregressions. Journal of Economic Dynamics and Control, 28, 349–366, doi:10.1016/S0165-1889(02)00168-9.

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)
set.seed(123)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20, 2)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20, thin = 2) |> 
  compute_impulse_responses(horizon = 4) -> irf

Bayesian estimation of a homoskedastic Structural Vector Autoregression with t-distributed structural shocks via Gibbs sampler

Description

Estimates the homoskedastic SVAR using the Gibbs sampler proposed by Waggoner & Zha (2003) for the structural matrix B and the equation-by-equation sampler by Chan, Koop, & Yu (2024) for the autoregressive slope parameters A. The Robust Adaptive Metropolis algorithm by Vihola (2012) is used to the df parameter of the Student-t distribution. Additionally, the parameter matrices A and B follow a Minnesota prior and generalised-normal prior distributions respectively with the matrix-specific overall shrinkage parameters estimated using a hierarchical prior distribution as in Lütkepohl, Shang, Uzeda, and Woźniak (2024). See section Details for the model equations.

Usage

## S3 method for class 'BSVART'
estimate(specification, S, thin = 1, show_progress = TRUE)

Arguments

specification

an object of class BSVART generated using the specify_bsvar_t$new() function.

S

a positive integer, the number of posterior draws to be generated

thin

a positive integer, specifying the frequency of MCMC output thinning

show_progress

a logical value, if TRUE the estimation progress bar is visible

Details

The homoskedastic SVAR model with t-distributed structural shocks is given by the reduced form equation:

Y = AX + E

The structural equation is given by

BE = U

where U is an NxT matrix of structural form error terms, and B is an NxN matrix of contemporaneous relationships.

Finally, the structural shocks, U, are temporally and contemporaneously independent and jointly Student-t distributed with zero mean, unit variances, and an estimated degrees-of-freedom parameter.

Value

An object of class PosteriorBSVART containing the Bayesian estimation output and containing two elements:

posterior a list with a collection of S draws from the posterior distribution generated via Gibbs sampler containing:

A: an NxKxS array with the posterior draws for matrix A
B: an NxNxS array with the posterior draws for matrix B
hyper: a 5xS matrix with the posterior draws for the hyper-parameters of the hierarchical prior distribution
df: an S vector with the posterior draws for the degrees-of-freedom parameter of the Student-t distribution
lambda: a TxS matrix with the posterior draws for the latent variable

last_draw an object of class BSVART with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Chan, J.C.C., Koop, G, and Yu, X. (2024) Large Order-Invariant Bayesian VARs with Stochastic Volatility. Journal of Business & Economic Statistics, 42, doi:10.1080/07350015.2023.2252039.

Waggoner, D.F., and Zha, T., (2003) A Gibbs sampler for structural vector autoregressions. Journal of Economic Dynamics and Control, 28, 349–366, doi:10.1016/S0165-1889(02)00168-9.

Vihola, M. (2012) Robust adaptive Metropolis algorithm with coerced acceptance rate. Statistics & Computing, 22, 997–1008, doi:10.1007/s11222-011-9269-5.

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_t$new(us_fiscal_lsuw, p = 4)

# run the burn-in
burn_in        = estimate(specification, 5)

# estimate the model
posterior      = estimate(burn_in, 10, thin = 2)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_t$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 10, thin = 2) -> posterior

Bayesian estimation of a homoskedastic Structural Vector Autoregression via Gibbs sampler

Description

Usage

## S3 method for class 'PosteriorBSVAR'
estimate(specification, S, thin = 1, show_progress = TRUE)

Arguments

specification

an object of class PosteriorBSVAR generated using the estimate.BSVAR() function. This setup facilitates the continuation of the MCMC sampling starting from the last draw of the previous run.

S

a positive integer, the number of posterior draws to be generated

thin

a positive integer, specifying the frequency of MCMC output thinning

show_progress

a logical value, if TRUE the estimation progress bar is visible

Details

The homoskedastic SVAR model is given by the reduced form equation:

Y = AX + E

The structural equation is given by

BE = U

where U is an NxT matrix of structural form error terms, and B is an NxN matrix of contemporaneous relationships.

Finally, the structural shocks, U, are temporally and contemporaneously independent and jointly normally distributed with zero mean and unit variances.

Value

An object of class PosteriorBSVAR containing the Bayesian estimation output and containing two elements:

posterior a list with a collection of S draws from the posterior distribution generated via Gibbs sampler containing:

A: an NxKxS array with the posterior draws for matrix A
B: an NxNxS array with the posterior draws for matrix B
hyper: a 5xS matrix with the posterior draws for the hyper-parameters of the hierarchical prior distribution

last_draw an object of class BSVAR with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Chan, J.C.C., Koop, G, and Yu, X. (2024) Large Order-Invariant Bayesian VARs with Stochastic Volatility. Journal of Business & Economic Statistics, 42, doi:10.1080/07350015.2023.2252039.

Waggoner, D.F., and Zha, T., (2003) A Gibbs sampler for structural vector autoregressions. Journal of Economic Dynamics and Control, 28, 349–366, doi:10.1016/S0165-1889(02)00168-9.

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)
set.seed(123)

# run the burn-in
burn_in        = estimate(specification, 5)

# estimate the model
posterior      = estimate(burn_in, 10, thin = 2)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 10, thin = 2) |> 
  compute_impulse_responses(horizon = 4) -> irf

Bayesian estimation of a Structural Vector Autoregression with shocks following a finite mixture of normal components via Gibbs sampler

Description

Usage

## S3 method for class 'PosteriorBSVARMIX'
estimate(specification, S, thin = 1, show_progress = TRUE)

Arguments

specification

an object of class PosteriorBSVARMIX generated using the estimate.BSVAR() function. This setup facilitates the continuation of the MCMC sampling starting from the last draw of the previous run.

S

a positive integer, the number of posterior draws to be generated

thin

a positive integer, specifying the frequency of MCMC output thinning

show_progress

a logical value, if TRUE the estimation progress bar is visible

Details

The heteroskedastic SVAR model is given by the reduced form equation:

Y = AX + E

The structural equation is given by

BE = U

where U is an NxT matrix of structural form error terms, and B is an NxN matrix of contemporaneous relationships.

Var_{t-1}[u_{n.t}] = s^2_{n.s_t}

where s_t is a the regime indicator of the regime-specific conditional variances of structural shocks s^2_{n.s_t}. In this model, the variances of each of the structural shocks sum to M.

The regime indicator s_t is either such that:

the regime probabilities are non-zero which requires all regimes to have a positive number occurrences over the sample period, or
sparse with potentially many regimes with zero occurrences over the sample period and in which the number of regimes is estimated.

These model selection also with this respect is made using function specify_bsvar_mix.

Value

An object of class PosteriorBSVARMIX containing the Bayesian estimation output and containing two elements:

posterior a list with a collection of S draws from the posterior distribution generated via Gibbs sampler containing:

A: an NxKxS array with the posterior draws for matrix A
B: an NxNxS array with the posterior draws for matrix B
hyper: a 5xS matrix with the posterior draws for the hyper-parameters of the hierarchical prior distribution
sigma2: an NxMxS array with the posterior draws for the structural shocks conditional variances
PR_TR: an MxMxS array with the posterior draws for the transition matrix.
xi: an MxTxS array with the posterior draws for the regime allocation matrix.
pi_0: an MxS matrix with the posterior draws for the ergodic probabilities
sigma: an NxTxS array with the posterior draws for the structural shocks conditional standard deviations' series over the sample period

last_draw an object of class BSVARMIX with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Chan, J.C.C., Koop, G, and Yu, X. (2024) Large Order-Invariant Bayesian VARs with Stochastic Volatility. Journal of Business & Economic Statistics, 42, doi:10.1080/07350015.2023.2252039.

Song, Y., and Woźniak, T., (2021) Markov Switching. Oxford Research Encyclopedia of Economics and Finance, Oxford University Press, doi:10.1093/acrefore/9780190625979.013.174.

Waggoner, D.F., and Zha, T., (2003) A Gibbs sampler for structural vector autoregressions. Journal of Economic Dynamics and Control, 28, 349–366, doi:10.1016/S0165-1889(02)00168-9.

Woźniak, T., and Droumaguet, M., (2024) Bayesian Assessment of Identifying Restrictions for Heteroskedastic Structural VARs

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 1, M = 2)
set.seed(123)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20, thin = 2)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_mix$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  estimate(S = 20, thin = 2) |> 
  compute_impulse_responses(horizon = 4) -> irf

Bayesian estimation of a Structural Vector Autoregression with Markov-switching heteroskedasticity via Gibbs sampler

Description

Usage

## S3 method for class 'PosteriorBSVARMSH'
estimate(specification, S, thin = 1, show_progress = TRUE)

Arguments

specification

an object of class PosteriorBSVARMSH generated using the estimate.BSVAR() function. This setup facilitates the continuation of the MCMC sampling starting from the last draw of the previous run.

S

a positive integer, the number of posterior draws to be generated

thin

a positive integer, specifying the frequency of MCMC output thinning

show_progress

a logical value, if TRUE the estimation progress bar is visible

Details

The heteroskedastic SVAR model is given by the reduced form equation:

Y = AX + E

The structural equation is given by

BE = U

where U is an NxT matrix of structural form error terms, and B is an NxN matrix of contemporaneous relationships.

Var_{t-1}[u_{n.t}] = s^2_{n.s_t}

The Markov process s_t is either:

stationary, irreducible, and aperiodic which requires all regimes to have a positive number occurrences over the sample period, or
sparse with potentially many regimes with zero occurrences over the sample period and in which the number of regimes is estimated.

These model selection also with this respect is made using function specify_bsvar_msh.

Value

An object of class PosteriorBSVARMSH containing the Bayesian estimation output and containing two elements:

posterior a list with a collection of S draws from the posterior distribution generated via Gibbs sampler containing:

A: an NxKxS array with the posterior draws for matrix A
B: an NxNxS array with the posterior draws for matrix B
hyper: a 5xS matrix with the posterior draws for the hyper-parameters of the hierarchical prior distribution
sigma2: an NxMxS array with the posterior draws for the structural shocks conditional variances
PR_TR: an MxMxS array with the posterior draws for the transition matrix.
xi: an MxTxS array with the posterior draws for the regime allocation matrix.
pi_0: an MxS matrix with the posterior draws for the initial state probabilities
sigma: an NxTxS array with the posterior draws for the structural shocks conditional standard deviations' series over the sample period

last_draw an object of class BSVARMSH with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Chan, J.C.C., Koop, G, and Yu, X. (2024) Large Order-Invariant Bayesian VARs with Stochastic Volatility. Journal of Business & Economic Statistics, 42, doi:10.1080/07350015.2023.2252039.

Song, Y., and Woźniak, T., (2021) Markov Switching. Oxford Research Encyclopedia of Economics and Finance, Oxford University Press, doi:10.1093/acrefore/9780190625979.013.174.

Waggoner, D.F., and Zha, T., (2003) A Gibbs sampler for structural vector autoregressions. Journal of Economic Dynamics and Control, 28, 349–366, doi:10.1016/S0165-1889(02)00168-9.

Woźniak, T., and Droumaguet, M., (2024) Bayesian Assessment of Identifying Restrictions for Heteroskedastic Structural VARs

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 1, M = 2)
set.seed(123)

# run the burn-in
burn_in        = estimate(specification, 5)

# estimate the model
posterior      = estimate(burn_in, 10, thin = 2)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new(p = 1, M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 10, thin = 2) |> 
  compute_impulse_responses(horizon = 4) -> irf

Bayesian estimation of a Structural Vector Autoregression with Stochastic Volatility heteroskedasticity via Gibbs sampler

Description

Usage

## S3 method for class 'PosteriorBSVARSV'
estimate(specification, S, thin = 1, show_progress = TRUE)

Arguments

specification

an object of class PosteriorBSVARSV generated using the estimate.BSVAR() function. This setup facilitates the continuation of the MCMC sampling starting from the last draw of the previous run.

S

a positive integer, the number of posterior draws to be generated

thin

a positive integer, specifying the frequency of MCMC output thinning

show_progress

a logical value, if TRUE the estimation progress bar is visible

Details

The heteroskedastic SVAR model is given by the reduced form equation:

Y = AX + E

The structural equation is given by

BE = U

Var_{t-1}[u_{n.t}] = exp(w_n h_{n.t})

where w_n is the estimated conditional standard deviation of the log-conditional variance and the log-volatility process h_{n.t} follows an autoregressive process:

h_{n.t} = g_n h_{n.t-1} + v_{n.t}

where h_{n.0}=0, g_n is an autoregressive parameter and v_{n.t} is a standard normal error term.

The centred Stochastic Volatility by Chan, Koop, & Yu (2021) is selected by setting argument centred_sv of function specify_bsvar_sv$new() to value TRUE. Its conditional variances are given by:

Var_{t-1}[u_{n.t}] = exp(h_{n.t})

where the log-conditional variances h_{n.t} follow an autoregressive process:

h_{n.t} = g_n h_{n.t-1} + v_{n.t}

where h_{n.0}=0, g_n is an autoregressive parameter and v_{n.t} is a zero-mean normal error term with variance s_{v.n}^2.

Value

An object of class PosteriorBSVARSV containing the Bayesian estimation output and containing two elements:

posterior a list with a collection of S draws from the posterior distribution generated via Gibbs sampler containing:

A: an NxKxS array with the posterior draws for matrix A
B: an NxNxS array with the posterior draws for matrix B
hyper: a 5xS matrix with the posterior draws for the hyper-parameters of the hierarchical prior distribution
h: an NxTxS array with the posterior draws of the log-volatility processes
rho: an NxS matrix with the posterior draws of SV autoregressive parameters
omega: an NxS matrix with the posterior draws of SV process conditional standard deviations
S: an NxTxS array with the posterior draws of the auxiliary mixture component indicators
sigma2_omega: an NxS matrix with the posterior draws of the variances of the zero-mean normal prior for omega
s_: an S-vector with the posterior draws of the scale of the gamma prior of the hierarchical prior for sigma2_omega

last_draw an object of class BSVARSV with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Chan, J.C.C., Koop, G, and Yu, X. (2024) Large Order-Invariant Bayesian VARs with Stochastic Volatility. Journal of Business & Economic Statistics, 42, doi:10.1080/07350015.2023.2252039.

Waggoner, D.F., and Zha, T., (2003) A Gibbs sampler for structural vector autoregressions. Journal of Economic Dynamics and Control, 28, 349–366, doi:10.1016/S0165-1889(02)00168-9.

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)
set.seed(123)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20, 2)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1) |>
  estimate(S = 10) |> 
  estimate(S = 20, thin = 2) |> 
  compute_impulse_responses(horizon = 4) -> irf

Bayesian estimation of a homoskedastic Structural Vector Autoregression with t-distributed structural shocks via Gibbs sampler

Description

Estimates the homoskedastic SVAR using the Gibbs sampler proposed by Waggoner & Zha (2003) for the structural matrix B and the equation-by-equation sampler by Chan, Koop, & Yu (2024) for the autoregressive slope parameters A. The Robust Adaptive Metropolis algorithm by Vihola (2012) is used to the df parameter of the Student-t distribution. Additionally, the parameter matrices A and B follow a Minnesota prior and generalised-normal prior distributions respectively with the matrix-specific overall shrinkage parameters estimated using a hierarchical prior distribution as in Lütkepohl, Shang, Uzeda, and Woźniak (2024). See section Details for the model equations.

Usage

## S3 method for class 'PosteriorBSVART'
estimate(specification, S, thin = 1, show_progress = TRUE)

Arguments

specification

an object of class PosteriorBSVART generated using the estimate.BSVART() function. This setup facilitates the continuation of the MCMC sampling starting from the last draw of the previous run.

S

a positive integer, the number of posterior draws to be generated

thin

a positive integer, specifying the frequency of MCMC output thinning

show_progress

a logical value, if TRUE the estimation progress bar is visible

Details

The homoskedastic SVAR model with t-distributed structural shocks is given by the reduced form equation:

Y = AX + E

The structural equation is given by

BE = U

where U is an NxT matrix of structural form error terms, and B is an NxN matrix of contemporaneous relationships.

Finally, the structural shocks, U, are temporally and contemporaneously independent and jointly Student-t distributed with zero mean, unit variances, and an estimated degrees-of-freedom parameter.

Value

An object of class PosteriorBSVART containing the Bayesian estimation output and containing two elements:

posterior a list with a collection of S draws from the posterior distribution generated via Gibbs sampler containing:

A: an NxKxS array with the posterior draws for matrix A
B: an NxNxS array with the posterior draws for matrix B
hyper: a 5xS matrix with the posterior draws for the hyper-parameters of the hierarchical prior distribution
df: an S vector with the posterior draws for the degrees-of-freedom parameter of the Student-t distribution
lambda: a TxS matrix with the posterior draws for the latent variable

last_draw an object of class BSVART with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Chan, J.C.C., Koop, G, and Yu, X. (2024) Large Order-Invariant Bayesian VARs with Stochastic Volatility. Journal of Business & Economic Statistics, 42, doi:10.1080/07350015.2023.2252039.

Waggoner, D.F., and Zha, T., (2003) A Gibbs sampler for structural vector autoregressions. Journal of Economic Dynamics and Control, 28, 349–366, doi:10.1016/S0165-1889(02)00168-9.

Vihola, M. (2012) Robust adaptive Metropolis algorithm with coerced acceptance rate. Statistics & Computing, 22, 997–1008, doi:10.1007/s11222-011-9269-5.

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_t$new(us_fiscal_lsuw, p = 1)
set.seed(123)

# run the burn-in
burn_in        = estimate(specification, 5)

# estimate the model
posterior      = estimate(burn_in, 10, thin = 2)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_t$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 10, thin = 2) -> posterior

Forecasting using Structural Vector Autoregression

Description

Samples from the joint predictive density of all of the dependent variables for models from packages bsvars, bsvarSIGNs or bvarPANELs at forecast horizons from 1 to horizon specified as an argument of the function.

Usage

forecast(posterior, horizon = 1, exogenous_forecast, conditional_forecast)

Arguments

posterior

posterior estimation outcome obtained by running the estimate function.

horizon

a positive integer, specifying the forecasting horizon.

exogenous_forecast

forecasted values of the exogenous variables.

conditional_forecast

forecasted values for selected variables.

Value

A list of class Forecasts containing the draws from the predictive density and for heteroskedastic models the draws from the predictive density of structural shocks conditional standard deviations and data. The output elements include:

forecasts: an NxTxS array with the draws from predictive density
forecasts_sigma: provided only for heteroskedastic models, an NxTxS array with the draws from the predictive density of structural shocks conditional standard deviations
Y: an NxT matrix with the data on dependent variables

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 5)

# estimate the model
posterior      = estimate(burn_in, 10)

# sample from predictive density 1 year ahead
predictive     = forecast(posterior, 4)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 10) |> 
  forecast(horizon = 4) -> predictive

# conditional forecasting using a model with exogenous variables
############################################################
data(us_fiscal_ex_forecasts)      # upload exogenous variables future values
data(us_fiscal_cond_forecasts)    # upload a matrix with projected ttr

#' set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1, exogenous = us_fiscal_ex)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 10)

# forecast 2 years ahead
predictive     = forecast(
                    posterior, 
                    horizon = 8,
                    exogenous_forecast = us_fiscal_ex_forecasts,
                    conditional_forecast = us_fiscal_cond_forecasts
                  )
summary(predictive)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1, exogenous = us_fiscal_ex) |>
  estimate(S = 5) |> 
  estimate(S = 10) |> 
  forecast(
    horizon = 8,
    exogenous_forecast = us_fiscal_ex_forecasts,
    conditional_forecast = us_fiscal_cond_forecasts
  ) |> plot()

Forecasting using Structural Vector Autoregression

Description

Usage

## S3 method for class 'PosteriorBSVAR'
forecast(
  posterior,
  horizon = 1,
  exogenous_forecast = NULL,
  conditional_forecast = NULL
)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVAR obtained by running the estimate function.

horizon

a positive integer, specifying the forecasting horizon.

exogenous_forecast

a matrix of dimension horizon x d containing forecasted values of the exogenous variables.

conditional_forecast

a horizon x N matrix with forecasted values for selected variables. It should only contain numeric or NA values. The entries with NA values correspond to the values that are forecasted conditionally on the realisations provided as numeric values.

Value

A list of class Forecasts containing the draws from the predictive density and data. The output list includes element:

forecasts: an NxTxS array with the draws from predictive density
Y: an NxT matrix with the data on dependent variables

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 5)

# estimate the model
posterior      = estimate(burn_in, 10)

# sample from predictive density 1 year ahead
predictive     = forecast(posterior, 4)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 10) |> 
  forecast(horizon = 4) -> predictive

# conditional forecasting using a model with exogenous variables
############################################################
data(us_fiscal_ex_forecasts)      # upload exogenous variables future values
data(us_fiscal_cond_forecasts)    # upload a matrix with projected ttr

#' set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1, exogenous = us_fiscal_ex)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 10)

# forecast 2 years ahead
predictive     = forecast(
                    posterior, 
                    horizon = 8,
                    exogenous_forecast = us_fiscal_ex_forecasts,
                    conditional_forecast = us_fiscal_cond_forecasts
                  )
summary(predictive)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1, exogenous = us_fiscal_ex) |>
  estimate(S = 5) |> 
  estimate(S = 10) |> 
  forecast(
    horizon = 8,
    exogenous_forecast = us_fiscal_ex_forecasts,
    conditional_forecast = us_fiscal_cond_forecasts
  ) |> plot()

Forecasting using Structural Vector Autoregression

Description

Usage

## S3 method for class 'PosteriorBSVARMIX'
forecast(
  posterior,
  horizon = 1,
  exogenous_forecast = NULL,
  conditional_forecast = NULL
)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARMIX obtained by running the estimate function.

horizon

a positive integer, specifying the forecasting horizon.

exogenous_forecast

a matrix of dimension horizon x d containing forecasted values of the exogenous variables.

conditional_forecast

Value

forecasts: an NxTxS array with the draws from predictive density
forecasts_sigma: provided only for heteroskedastic models, an NxTxS array with the draws from the predictive density of structural shocks conditional standard deviations
Y: an NxT matrix with the data on dependent variables

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 1, M = 2)

# run the burn-in
burn_in        = estimate(specification, 5)

# estimate the model
posterior      = estimate(burn_in, 10)

# sample from predictive density 1 year ahead
predictive     = forecast(posterior, 4)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_mix$new(p = 1, M = 2) |>
  estimate(S = 5) |>
  estimate(S = 10) |>  
  forecast(horizon = 4) -> predictive
  
# conditional forecasting using a model with exogenous variables
############################################################
data(us_fiscal_ex_forecasts)      # upload exogenous variables future values
data(us_fiscal_cond_forecasts)    # upload a matrix with projected ttr

#' set.seed(123)
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, M = 2, exogenous = us_fiscal_ex)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 10)

# forecast 2 years ahead
predictive     = forecast(
                    posterior, 
                    horizon = 8,
                    exogenous_forecast = us_fiscal_ex_forecasts,
                    conditional_forecast = us_fiscal_cond_forecasts
                  )
summary(predictive)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_mix$new(M = 2, exogenous = us_fiscal_ex) |>
  estimate(S = 5) |> 
  estimate(S = 10) |> 
  forecast(
    horizon = 8,
    exogenous_forecast = us_fiscal_ex_forecasts,
    conditional_forecast = us_fiscal_cond_forecasts
  ) |> plot()

Forecasting using Structural Vector Autoregression

Description

Usage

## S3 method for class 'PosteriorBSVARMSH'
forecast(
  posterior,
  horizon = 1,
  exogenous_forecast = NULL,
  conditional_forecast = NULL
)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARMSH obtained by running the estimate function.

horizon

a positive integer, specifying the forecasting horizon.

exogenous_forecast

a matrix of dimension horizon x d containing forecasted values of the exogenous variables.

conditional_forecast

Value

forecasts: an NxTxS array with the draws from predictive density
forecasts_sigma: provided only for heteroskedastic models, an NxTxS array with the draws from the predictive density of structural shocks conditional standard deviations
Y: an NxT matrix with the data on dependent variables

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 1, M = 2)

# run the burn-in
burn_in        = estimate(specification, 5)

# estimate the model
posterior      = estimate(burn_in, 10)

# sample from predictive density 1 year ahead
predictive     = forecast(posterior, 4)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new(p = 1, M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 10) |> 
  forecast(horizon = 4) -> predictive
  
# conditional forecasting using a model with exogenous variables
############################################################
data(us_fiscal_ex_forecasts)      # upload exogenous variables future values
data(us_fiscal_cond_forecasts)    # upload a matrix with projected ttr

#' set.seed(123)
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, M = 2, exogenous = us_fiscal_ex)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 10)

# forecast 2 years ahead
predictive     = forecast(
                    posterior, 
                    horizon = 8,
                    exogenous_forecast = us_fiscal_ex_forecasts,
                    conditional_forecast = us_fiscal_cond_forecasts
                  )
summary(predictive)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new(M = 2, exogenous = us_fiscal_ex) |>
  estimate(S = 5) |> 
  estimate(S = 10) |> 
  forecast(
    horizon = 8,
    exogenous_forecast = us_fiscal_ex_forecasts,
    conditional_forecast = us_fiscal_cond_forecasts
  ) |> plot()

Forecasting using Structural Vector Autoregression

Description

Usage

## S3 method for class 'PosteriorBSVARSV'
forecast(
  posterior,
  horizon = 1,
  exogenous_forecast = NULL,
  conditional_forecast = NULL
)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVARSV obtained by running the estimate function.

horizon

a positive integer, specifying the forecasting horizon.

exogenous_forecast

a matrix of dimension horizon x d containing forecasted values of the exogenous variables.

conditional_forecast

Value

forecasts: an NxTxS array with the draws from predictive density
forecasts_sigma: provided only for heteroskedastic models, an NxTxS array with the draws from the predictive density of structural shocks conditional standard deviations
Y: an NxT matrix with the data on dependent variables

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 5)

# estimate the model
posterior      = estimate(burn_in, 5)

# sample from predictive density 1 year ahead
predictive     = forecast(posterior, 2)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1) |>
  estimate(S = 5) |>
  estimate(S = 5) |>  
  forecast(horizon = 2) -> predictive
  
# conditional forecasting using a model with exogenous variables
############################################################
data(us_fiscal_ex_forecasts)      # upload exogenous variables future values
data(us_fiscal_cond_forecasts)    # upload a matrix with projected ttr

#' set.seed(123)
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, exogenous = us_fiscal_ex)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 10)

# forecast 2 years ahead
predictive     = forecast(
                    posterior, 
                    horizon = 8,
                    exogenous_forecast = us_fiscal_ex_forecasts,
                    conditional_forecast = us_fiscal_cond_forecasts
                  )
summary(predictive)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new(exogenous = us_fiscal_ex) |>
  estimate(S = 5) |> 
  estimate(S = 10) |> 
  forecast(
    horizon = 8,
    exogenous_forecast = us_fiscal_ex_forecasts,
    conditional_forecast = us_fiscal_cond_forecasts
  ) |> plot()

Forecasting using Structural Vector Autoregression

Description

Usage

## S3 method for class 'PosteriorBSVART'
forecast(
  posterior,
  horizon = 1,
  exogenous_forecast = NULL,
  conditional_forecast = NULL
)

Arguments

posterior

posterior estimation outcome - an object of class PosteriorBSVART obtained by running the estimate function.

horizon

a positive integer, specifying the forecasting horizon.

exogenous_forecast

a matrix of dimension horizon x d containing forecasted values of the exogenous variables.

conditional_forecast

Value

A list of class Forecasts containing the draws from the predictive density and data. The output list includes element:

forecasts: an NxTxS array with the draws from predictive density
Y: an NxT matrix with the data on dependent variables

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_t$new(us_fiscal_lsuw, p = 1)

# run the burn-in
burn_in        = estimate(specification, 5)

# estimate the model
posterior      = estimate(burn_in, 10)

# sample from predictive density 1 year ahead
predictive     = forecast(posterior, 4)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_t$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 10) |> 
  forecast(horizon = 4) -> predictive

# conditional forecasting using a model with exogenous variables
############################################################
data(us_fiscal_ex_forecasts)      # upload exogenous variables future values
data(us_fiscal_cond_forecasts)    # upload a matrix with projected ttr

#' set.seed(123)
specification  = specify_bsvar_t$new(us_fiscal_lsuw, exogenous = us_fiscal_ex)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 10)

# forecast 2 years ahead
predictive     = forecast(
                    posterior, 
                    horizon = 8,
                    exogenous_forecast = us_fiscal_ex_forecasts,
                    conditional_forecast = us_fiscal_cond_forecasts
                  )
summary(predictive)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_t$new(exogenous = us_fiscal_ex) |>
  estimate(S = 5) |> 
  estimate(S = 10) |> 
  forecast(
    horizon = 8,
    exogenous_forecast = us_fiscal_ex_forecasts,
    conditional_forecast = us_fiscal_cond_forecasts
  ) |> plot()

Waggoner & Zha (2003) row signs normalisation of the posterior draws for matrix `B`

Description

Normalises the sign of rows of matrix B MCMC draws, provided as the first argument posterior_B, relative to matrix B_hat, provided as the second argument of the function. The implemented procedure proposed by Waggoner, Zha (2003) normalises the MCMC output in an optimal way leading to the unimodal posterior. Only normalised MCMC output is suitable for the computations of the posterior characteristics of the B matrix elements and their functions such as the impulse response functions and other economically interpretable values.

Usage

normalise_posterior(posterior, B_hat)

Arguments

posterior

posterior estimation outcome - an object of either of classes: PosteriorBSVAR, PosteriorBSVARMSH, PosteriorBSVARMIX, or PosteriorBSVARSV containing, amongst other draws, the S draws from the posterior distribution of the NxN matrix of contemporaneous relationships B. These draws are to be normalised with respect to:

B_hat

an NxN matrix specified by the user to have the desired row signs

Value

Nothing. The normalised elements overwrite the corresponding elements of the first argument posterior_B by reference.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Waggoner, D.F., and Zha, T., (2003) Likelihood Preserving Normalization in Multiple Equation Models. Journal of Econometrics, 114(2), 329–47, doi:10.1016/S0304-4076(03)00087-3.

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 4)
set.seed(123)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 10, thin = 1)

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag((-1) * sign(diag(BB))) %*% BB         # set negative diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

Plots fitted values of dependent variables

Description

Plots of fitted values of dependent variables including their median and percentiles.

Usage

## S3 method for class 'Forecasts'
plot(
  x,
  probability = 0.9,
  data_in_plot = 1,
  col = "#ff69b4",
  main,
  xlab,
  mar.multi = c(1, 4.6, 0, 2.1),
  oma.multi = c(6, 0, 5, 0),
  ...
)

Arguments

x

an object of class Forecasts obtained using the forecast() function containing posterior draws of fitted values of dependent variables.

probability

a parameter determining the interval to be plotted. The interval stretches from the 0.5 * (1 - probability) to 1 - 0.5 * (1 - probability) percentile of the posterior distribution.

data_in_plot

a fraction value in the range (0, 1) determining how many of the last observations in the data should be plotted with the forecasts.

col

a colour of the plot line and the ribbon

main

an alternative main title for the plot

xlab

an alternative x-axis label for the plot

mar.multi

the default mar argument setting in graphics::par. Modify with care!

oma.multi

the default oma argument setting in graphics::par. Modify with care!

...

additional arguments affecting the summary produced.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

data(us_fiscal_lsuw)                                  # upload data
set.seed(123)                                         # set seed
specification  = specify_bsvar$new(us_fiscal_lsuw)    # specify model
burn_in        = estimate(specification, 10)          # run the burn-in
posterior      = estimate(burn_in, 20, thin = 1)      # estimate the model

# compute forecasts
fore            = forecast(posterior, horizon = 4)
plot(fore)                                            # plot forecasts

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 10) |> 
  estimate(S = 20, thin = 1) |> 
  forecast(horizon = 4) |>
  plot()

Plots forecast error variance decompositions

Description

Plots of the posterior means of the forecast error variance decompositions.

Usage

## S3 method for class 'PosteriorFEVD'
plot(
  x,
  shock_names,
  cols,
  main,
  xlab,
  mar.multi = c(1, 4.6, 0, 4.6),
  oma.multi = c(6, 0, 5, 0),
  ...
)

Arguments

x

an object of class PosteriorFEVD obtained using the compute_variance_decompositions() function containing posterior draws of forecast error variance decompositions.

shock_names

a vector of length N containing names of the structural shocks.

cols

an N-vector with colours of the plot

main

an alternative main title for the plot

xlab

an alternative x-axis label for the plot

mar.multi

the default mar argument setting in graphics::par. Modify with care!

oma.multi

the default oma argument setting in graphics::par. Modify with care!

...

additional arguments affecting the summary produced.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

data(us_fiscal_lsuw)                                  # upload data
set.seed(123)                                         # set seed
specification  = specify_bsvar$new(us_fiscal_lsuw)    # specify model
burn_in        = estimate(specification, 10)          # run the burn-in
posterior      = estimate(burn_in, 20, thin = 1)      # estimate the model

# compute forecast error variance decompositions
fevd           = compute_variance_decompositions(posterior, horizon = 4)
plot(fevd)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 10) |> 
  estimate(S = 20, thin = 1) |> 
  compute_variance_decompositions(horizon = 4) |>
  plot()

Plots fitted values of dependent variables

Description

Plots of fitted values of dependent variables including their median and percentiles.

Usage

## S3 method for class 'PosteriorFitted'
plot(
  x,
  probability = 0.9,
  col = "#ff69b4",
  main,
  xlab,
  mar.multi = c(1, 4.6, 0, 2.1),
  oma.multi = c(6, 0, 5, 0),
  ...
)

Arguments

x

an object of class PosteriorFitted obtained using the compute_fitted_values() function containing posterior draws of fitted values of dependent variables.

probability

a parameter determining the interval to be plotted. The interval stretches from the 0.5 * (1 - probability) to 1 - 0.5 * (1 - probability) percentile of the posterior distribution.

col

a colour of the plot line and the ribbon

main

an alternative main title for the plot

xlab

an alternative x-axis label for the plot

mar.multi

the default mar argument setting in graphics::par. Modify with care!

oma.multi

the default oma argument setting in graphics::par. Modify with care!

...

additional arguments affecting the summary produced.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

data(us_fiscal_lsuw)                                  # upload data
set.seed(123)                                         # set seed
specification  = specify_bsvar$new(us_fiscal_lsuw)    # specify model
burn_in        = estimate(specification, 10)          # run the burn-in
posterior      = estimate(burn_in, 20, thin = 1)      # estimate the model

# compute fitted values
fitted         = compute_fitted_values(posterior)
plot(fitted)                                          # plot fitted values

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 10) |> 
  estimate(S = 20, thin = 1) |> 
  compute_fitted_values() |>
  plot()

Plots historical decompositions

Description

Plots of the posterior means of the historical decompositions.

Usage

## S3 method for class 'PosteriorHD'
plot(
  x,
  shock_names,
  cols,
  main,
  xlab,
  mar.multi = c(1, 4.6, 0, 4.6),
  oma.multi = c(6, 0, 5, 0),
  ...
)

Arguments

x

an object of class PosteriorHD obtained using the compute_historical_decompositions() function containing posterior draws of historical decompositions.

shock_names

a vector of length N containing names of the structural shocks.

cols

an N-vector with colours of the plot

main

an alternative main title for the plot

xlab

an alternative x-axis label for the plot

mar.multi

the default mar argument setting in graphics::par. Modify with care!

oma.multi

the default oma argument setting in graphics::par. Modify with care!

...

additional arguments affecting the summary produced.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

data(us_fiscal_lsuw)                                  # upload data
set.seed(123)                                         # set seed
specification  = specify_bsvar$new(us_fiscal_lsuw)    # specify model
burn_in        = estimate(specification, 10)          # run the burn-in
posterior      = estimate(burn_in, 20, thin = 1)      # estimate the model

# compute historical decompositions
fevd           = compute_historical_decompositions(posterior)
plot(fevd)                                            

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 10) |> 
  estimate(S = 20, thin = 1) |> 
  compute_historical_decompositions() |>
  plot()

Plots impulse responses

Description

Plots of of all variables to all shocks including their median and percentiles.

Usage

## S3 method for class 'PosteriorIR'
plot(
  x,
  probability = 0.9,
  shock_names,
  col = "#ff69b4",
  main,
  xlab,
  mar.multi = c(1, 4.1, 0, 1.1),
  oma.multi = c(6, 0, 5, 0),
  ...
)

Arguments

x

an object of class PosteriorIR obtained using the compute_impulse_responses() function containing posterior draws of impulse responses.

probability

a parameter determining the interval to be plotted. The interval stretches from the 0.5 * (1 - probability) to 1 - 0.5 * (1 - probability) percentile of the posterior distribution.

shock_names

a vector of length N containing names of the structural shocks.

col

a colour of the plot line and the ribbon

main

an alternative main title for the plot

xlab

an alternative x-axis label for the plot

mar.multi

the default mar argument setting in graphics::par. Modify with care!

oma.multi

the default oma argument setting in graphics::par. Modify with care!

...

additional arguments affecting the summary produced.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

data(us_fiscal_lsuw)                                  # upload data
set.seed(123)                                         # set seed
specification  = specify_bsvar$new(us_fiscal_lsuw)    # specify model
burn_in        = estimate(specification, 10)          # run the burn-in
posterior      = estimate(burn_in, 20, thin = 1)      # estimate the model

# compute impulse responses
fitted         = compute_impulse_responses(posterior, horizon = 4)
plot(fitted)                                          # plot

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 10) |> 
  estimate(S = 20, thin = 1) |> 
  compute_impulse_responses(horizon = 4) |>
  plot()

Plots estimated regime probabilities

Description

Plots of estimated regime probabilities of Markov-switching heteroskedasticity or allocations of normal-mixture components including their median and percentiles.

Usage

## S3 method for class 'PosteriorRegimePr'
plot(
  x,
  probability = 0.9,
  col = "#ff69b4",
  main,
  xlab,
  mar.multi = c(1, 4.6, 0, 2.1),
  oma.multi = c(6, 0, 5, 0),
  ...
)

Arguments

x

an object of class PosteriorRegimePr obtained using the compute_regime_probabilities() function containing posterior draws of regime probabilities.

probability

a parameter determining the interval to be plotted. The interval stretches from the 0.5 * (1 - probability) to 1 - 0.5 * (1 - probability) percentile of the posterior distribution.

col

a colour of the plot line and the ribbon

main

an alternative main title for the plot

xlab

an alternative x-axis label for the plot

mar.multi

the default mar argument setting in graphics::par. Modify with care!

oma.multi

the default oma argument setting in graphics::par. Modify with care!

...

additional arguments affecting the summary produced.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

data(us_fiscal_lsuw)                                  # upload data
set.seed(123)                                         # set seed
specification  = specify_bsvar_msh$new(us_fiscal_lsuw)# specify model
burn_in        = estimate(specification, 10)          # run the burn-in
posterior      = estimate(burn_in, 20, thin = 1)      # estimate the model

# compute regime probabilities
rp             = compute_regime_probabilities(posterior)
plot(rp)                                              # plot

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new() |>
  estimate(S = 10) |> 
  estimate(S = 20, thin = 1) |> 
  compute_regime_probabilities() |>
  plot()

Plots structural shocks

Description

Plots of structural shocks including their median and percentiles.

Usage

## S3 method for class 'PosteriorShocks'
plot(
  x,
  probability = 0.9,
  col = "#ff69b4",
  main,
  xlab,
  mar.multi = c(1, 4.6, 0, 2.1),
  oma.multi = c(6, 0, 5, 0),
  ...
)

Arguments

x

an object of class PosteriorShocks obtained using the compute_structural_shocks() function containing posterior draws of structural shocks.

probability

a parameter determining the interval to be plotted. The interval stretches from the 0.5 * (1 - probability) to 1 - 0.5 * (1 - probability) percentile of the posterior distribution.

col

a colour of the plot line and the ribbon

main

an alternative main title for the plot

xlab

an alternative x-axis label for the plot

mar.multi

the default mar argument setting in graphics::par. Modify with care!

oma.multi

the default oma argument setting in graphics::par. Modify with care!

...

additional arguments affecting the summary produced.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

data(us_fiscal_lsuw)                                  # upload data
set.seed(123)                                         # set seed
specification  = specify_bsvar$new(us_fiscal_lsuw)    # specify model
burn_in        = estimate(specification, 10)          # run the burn-in
posterior      = estimate(burn_in, 20, thin = 1)      # estimate the model

# compute structural shocks
shocks         = compute_structural_shocks(posterior)
plot(shocks)                                          # plot

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 10) |> 
  estimate(S = 20, thin = 1) |> 
  compute_structural_shocks() |>
  plot()

Plots structural shocks' conditional standard deviations

Description

Plots of structural shocks' conditional standard deviations including their median and percentiles.

Usage

## S3 method for class 'PosteriorSigma'
plot(
  x,
  probability = 0.9,
  shock_names,
  col = "#ff69b4",
  main,
  xlab,
  mar.multi = c(1, 4.6, 0, 2.1),
  oma.multi = c(6, 0, 5, 0),
  ...
)

Arguments

x

an object of class PosteriorSigma obtained using the compute_conditional_sd() function containing posterior draws of conditional standard deviations of structural shocks.

probability

a parameter determining the interval to be plotted. The interval stretches from the 0.5 * (1 - probability) to 1 - 0.5 * (1 - probability) percentile of the posterior distribution.

shock_names

a vector of length N containing names of the structural shocks.

col

a colour of the plot line and the ribbon

main

an alternative main title for the plot

xlab

an alternative x-axis label for the plot

mar.multi

the default mar argument setting in graphics::par. Modify with care!

oma.multi

the default oma argument setting in graphics::par. Modify with care!

...

additional arguments affecting the summary produced.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

data(us_fiscal_lsuw)                                  # upload data
set.seed(123)                                         # set seed
specification  = specify_bsvar_sv$new(us_fiscal_lsuw) # specify model
burn_in        = estimate(specification, 5)           # run the burn-in
posterior      = estimate(burn_in, 5)                 # estimate the model

# compute structural shocks' conditional standard deviations
sigma          = compute_conditional_sd(posterior)
plot(sigma)                                            # plot conditional sds

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  compute_conditional_sd() |>
  plot()

Plots the median and an interval between two specified percentiles for a sequence of `K` random variables

Description

Plots the median and an interval between two specified percentiles for a sequence of K random variables based on the S posterior draws provided for each of them.

Usage

plot_ribbon(
  draws,
  probability = 0.9,
  col = "#ff69b4",
  ylim,
  ylab,
  xlab,
  start_at = 0,
  add = FALSE,
  ...
)

Arguments

draws

a K x S matrix with S posterior draws of K random variables, or a K x S x N array with N such matrices

probability

a number from interval (0,1) denoting the probability content of the plotted interval. The interval stretches from the 0.5 * (1 - probability) to 1 - 0.5 * (1 - probability) percentile of the posterior distribution.

col

a colour of the plot

ylim

the range of the y axis

ylab

the label of the y axis

xlab

the label of the x axis

start_at

an integer to denote the beginning of the x axis range

add

a logical value. If TRUE the current ribbon plot is added to an existing plot

...

other graphical parameters to be passed to base::plot

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

data(us_fiscal_lsuw)                                               # upload data
set.seed(123)                                                      # set seed
specification  = specify_bsvar$new(us_fiscal_lsuw)                 # specify model

burn_in        = estimate(specification, 10)                       # run the burn-in
posterior      = estimate(burn_in, 20, thin = 1)                   # estimate the model
irf            = compute_impulse_responses(posterior, horizon = 4) # impulse responses
plot_ribbon(irf[1,1,,])

R6 Class representing the specification of the homoskedastic BSVAR model

Description

The class BSVAR presents complete specification for the homoskedastic bsvar model.

Public fields

p: a non-negative integer specifying the autoregressive lag order of the model.
identification: an object IdentificationBSVAR with the identifying restrictions.
prior: an object PriorBSVAR with the prior specification.
data_matrices: an object DataMatricesBSVAR with the data matrices.
starting_values: an object StartingValuesBSVAR with the starting values.

Methods

Method `new()`

Create a new specification of the homoskedastic bsvar model BSVAR.

Usage

specify_bsvar$new(
  data,
  p = 1L,
  B,
  exogenous = NULL,
  stationary = rep(FALSE, ncol(data))
)

Arguments

data: a (T+p)xN matrix with time series data.
p: a positive integer providing model's autoregressive lag order.
B: a logical NxN matrix containing value TRUE for the elements of the structural matrix B to be estimated and value FALSE for exclusion restrictions to be set to zero.
exogenous: a (T+p)xd matrix of exogenous variables.
stationary: an N logical vector - its element set to FALSE sets the prior mean for the autoregressive parameters of the Nth equation to the white noise process, otherwise to random walk.

Returns

A new complete specification for the homoskedastic bsvar model BSVAR.

Method `get_data_matrices()`

Returns the data matrices as the DataMatricesBSVAR object.

Usage

specify_bsvar$get_data_matrices()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_data_matrices()

Method `get_identification()`

Returns the identifying restrictions as the IdentificationBSVARs object.

Usage

specify_bsvar$get_identification()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_identification()

Method `get_prior()`

Returns the prior specification as the PriorBSVAR object.

Usage

specify_bsvar$get_prior()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_prior()

Method `get_starting_values()`

Returns the starting values as the StartingValuesBSVAR object.

Usage

specify_bsvar$get_starting_values()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_starting_values()

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_bsvar$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar$new(
   data = us_fiscal_lsuw,
   p = 4
)


## ------------------------------------------------
## Method `specify_bsvar$get_data_matrices`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_data_matrices()


## ------------------------------------------------
## Method `specify_bsvar$get_identification`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_identification()


## ------------------------------------------------
## Method `specify_bsvar$get_prior`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_prior()


## ------------------------------------------------
## Method `specify_bsvar$get_starting_values`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_starting_values()

R6 Class representing the specification of the BSVAR model with a zero-mean mixture of normals model for structural shocks.

Description

The class BSVARMIX presents complete specification for the BSVAR model with a zero-mean mixture of normals model for structural shocks.

Super class

bsvars::BSVARMSH -> BSVARMIX

Public fields

p: a non-negative integer specifying the autoregressive lag order of the model.
identification: an object IdentificationBSVARs with the identifying restrictions.
prior: an object PriorBSVARMIX with the prior specification.
data_matrices: an object DataMatricesBSVAR with the data matrices.
starting_values: an object StartingValuesBSVARMIX with the starting values.
finiteM: a logical value - if true a finite mixture model is estimated. Otherwise, a sparse mixture model is estimated in which M=20 and the number of visited states is estimated.

Methods

Public methods

specify_bsvar_mix$new()
specify_bsvar_mix$clone()

Inherited methods

Method `new()`

Create a new specification of the BSVAR model with a zero-mean mixture of normals model for structural shocks, BSVARMIX.

Usage

specify_bsvar_mix$new(
  data,
  p = 1L,
  M = 2L,
  B,
  exogenous = NULL,
  stationary = rep(FALSE, ncol(data)),
  finiteM = TRUE
)

Arguments

data: a (T+p)xN matrix with time series data.
p: a positive integer providing model's autoregressive lag order.
M: an integer greater than 1 - the number of components of the mixture of normals.
B: a logical NxN matrix containing value TRUE for the elements of the structural matrix B to be estimated and value FALSE for exclusion restrictions to be set to zero.
exogenous: a (T+p)xd matrix of exogenous variables.
stationary: an N logical vector - its element set to FALSE sets the prior mean for the autoregressive parameters of the Nth equation to the white noise process, otherwise to random walk.
finiteM: a logical value - if true a finite mixture model is estimated. Otherwise, a sparse mixture model is estimated in which M=20 and the number of visited states is estimated.

Returns

A new complete specification for the bsvar model with a zero-mean mixture of normals model for structural shocks, BSVARMIX.

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_bsvar_mix$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_mix$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)

R6 Class representing the specification of the BSVAR model with Markov Switching Heteroskedasticity.

Description

The class BSVARMSH presents complete specification for the BSVAR model with Markov Switching Heteroskedasticity.

Public fields

p: a non-negative integer specifying the autoregressive lag order of the model.
identification: an object IdentificationBSVARs with the identifying restrictions.
prior: an object PriorBSVARMSH with the prior specification.
data_matrices: an object DataMatricesBSVAR with the data matrices.
starting_values: an object StartingValuesBSVARMSH with the starting values.
finiteM: a logical value - if true a stationary Markov switching model is estimated. Otherwise, a sparse Markov switching model is estimated in which M=20 and the number of visited states is estimated.

Methods

Public methods

specify_bsvar_msh$new()
specify_bsvar_msh$get_data_matrices()
specify_bsvar_msh$get_identification()
specify_bsvar_msh$get_prior()
specify_bsvar_msh$get_starting_values()
specify_bsvar_msh$clone()

Method `new()`

Create a new specification of the BSVAR model with Markov Switching Heteroskedasticity, BSVARMSH.

Usage

specify_bsvar_msh$new(
  data,
  p = 1L,
  M = 2L,
  B,
  exogenous = NULL,
  stationary = rep(FALSE, ncol(data)),
  finiteM = TRUE
)

Arguments

data: a (T+p)xN matrix with time series data.
p: a positive integer providing model's autoregressive lag order.
M: an integer greater than 1 - the number of Markov process' heteroskedastic regimes.
B: a logical NxN matrix containing value TRUE for the elements of the structural matrix B to be estimated and value FALSE for exclusion restrictions to be set to zero.
exogenous: a (T+p)xd matrix of exogenous variables.
stationary: an N logical vector - its element set to FALSE sets the prior mean for the autoregressive parameters of the Nth equation to the white noise process, otherwise to random walk.
finiteM: a logical value - if true a stationary Markov switching model is estimated. Otherwise, a sparse Markov switching model is estimated in which M=20 and the number of visited states is estimated.

Returns

A new complete specification for the bsvar model with Markov Switching Heteroskedasticity, BSVARMSH.

Method `get_data_matrices()`

Returns the data matrices as the DataMatricesBSVAR object.

Usage

specify_bsvar_msh$get_data_matrices()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_msh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$get_data_matrices()

Method `get_identification()`

Returns the identifying restrictions as the IdentificationBSVARs object.

Usage

specify_bsvar_msh$get_identification()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_msh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$get_identification()

Method `get_prior()`

Returns the prior specification as the PriorBSVARMSH object.

Usage

specify_bsvar_msh$get_prior()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_msh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$get_prior()

Method `get_starting_values()`

Returns the starting values as the StartingValuesBSVARMSH object.

Usage

specify_bsvar_msh$get_starting_values()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_msh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$get_starting_values()

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_bsvar_msh$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_msh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)


## ------------------------------------------------
## Method `specify_bsvar_msh$get_data_matrices`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar_msh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$get_data_matrices()


## ------------------------------------------------
## Method `specify_bsvar_msh$get_identification`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar_msh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$get_identification()


## ------------------------------------------------
## Method `specify_bsvar_msh$get_prior`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar_msh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$get_prior()


## ------------------------------------------------
## Method `specify_bsvar_msh$get_starting_values`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar_msh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$get_starting_values()

R6 Class representing the specification of the BSVAR model with Stochastic Volatility heteroskedasticity.

Description

The class BSVARSV presents complete specification for the BSVAR model with Stochastic Volatility heteroskedasticity.

Public fields

p: a non-negative integer specifying the autoregressive lag order of the model.
identification: an object IdentificationBSVARs with the identifying restrictions.
prior: an object PriorBSVARSV with the prior specification.
data_matrices: an object DataMatricesBSVAR with the data matrices.
starting_values: an object StartingValuesBSVARSV with the starting values.
centred_sv: a logical value - if true a centred parameterisation of the Stochastic Volatility process is estimated. Otherwise, its non-centred parameterisation is estimated. See Lütkepohl, Shang, Uzeda, Woźniak (2022) for more info.

Methods

Public methods

specify_bsvar_sv$new()
specify_bsvar_sv$get_data_matrices()
specify_bsvar_sv$get_identification()
specify_bsvar_sv$get_prior()
specify_bsvar_sv$get_starting_values()
specify_bsvar_sv$clone()

Method `new()`

Create a new specification of the BSVAR model with Stochastic Volatility heteroskedasticity, BSVARSV.

Usage

specify_bsvar_sv$new(
  data,
  p = 1L,
  B,
  exogenous = NULL,
  centred_sv = FALSE,
  stationary = rep(FALSE, ncol(data))
)

Arguments

data: a (T+p)xN matrix with time series data.
p: a positive integer providing model's autoregressive lag order.
B: a logical NxN matrix containing value TRUE for the elements of the structural matrix B to be estimated and value FALSE for exclusion restrictions to be set to zero.
exogenous: a (T+p)xd matrix of exogenous variables.
centred_sv: a logical value. If FALSE a non-centred Stochastic Volatility processes for conditional variances are estimated. Otherwise, a centred process is estimated.
stationary: an N logical vector - its element set to FALSE sets the prior mean for the autoregressive parameters of the Nth equation to the white noise process, otherwise to random walk.

Returns

A new complete specification for the bsvar model with Stochastic Volatility heteroskedasticity, BSVARSV.

Method `get_data_matrices()`

Returns the data matrices as the DataMatricesBSVAR object.

Usage

specify_bsvar_sv$get_data_matrices()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_sv$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_data_matrices()

Method `get_identification()`

Returns the identifying restrictions as the IdentificationBSVARs object.

Usage

specify_bsvar_sv$get_identification()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_sv$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_identification()

Method `get_prior()`

Returns the prior specification as the PriorBSVARSV object.

Usage

specify_bsvar_sv$get_prior()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_sv$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_prior()

Method `get_starting_values()`

Returns the starting values as the StartingValuesBSVARSV object.

Usage

specify_bsvar_sv$get_starting_values()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_sv$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_starting_values()

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_bsvar_sv$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_sv$new(
   data = us_fiscal_lsuw,
   p = 4
)


## ------------------------------------------------
## Method `specify_bsvar_sv$get_data_matrices`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar_sv$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_data_matrices()


## ------------------------------------------------
## Method `specify_bsvar_sv$get_identification`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar_sv$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_identification()


## ------------------------------------------------
## Method `specify_bsvar_sv$get_prior`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar_sv$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_prior()


## ------------------------------------------------
## Method `specify_bsvar_sv$get_starting_values`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar_sv$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_starting_values()

R6 Class representing the specification of the BSVAR model with t-distributed structural shocks.

Description

The class BSVART presents complete specification for the BSVAR model with t-distributed structural shocks.

Super class

bsvars::BSVAR -> BSVART

Public fields

p: a non-negative integer specifying the autoregressive lag order of the model.
identification: an object IdentificationBSVARs with the identifying restrictions.
prior: an object PriorBSVART with the prior specification.
data_matrices: an object DataMatricesBSVAR with the data matrices.
starting_values: an object StartingValuesBSVART with the starting values.
adaptiveMH: a vector of two values setting the Robust Adaptive Metropolis sampler for df: target acceptance rate and adaptive rate.

Methods

Public methods

specify_bsvar_t$new()
specify_bsvar_t$clone()

Inherited methods

Method `new()`

Create a new specification of the BSVAR model with t-distributed structural shocks, BSVART.

Usage

specify_bsvar_t$new(
  data,
  p = 1L,
  B,
  exogenous = NULL,
  stationary = rep(FALSE, ncol(data))
)

Arguments

data: a (T+p)xN matrix with time series data.
p: a positive integer providing model's autoregressive lag order.
B: a logical NxN matrix containing value TRUE for the elements of the structural matrix B to be estimated and value FALSE for exclusion restrictions to be set to zero.
exogenous: a (T+p)xd matrix of exogenous variables.
stationary: an N logical vector - its element set to FALSE sets the prior mean for the autoregressive parameters of the Nth equation to the white noise process, otherwise to random walk.

Returns

A new complete specification for the bsvar model with t-distributed structural shocks, BSVART.

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_bsvar_t$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_t$new(
   data = us_fiscal_lsuw,
   p = 4
)

R6 Class Representing DataMatricesBSVAR

Description

The class DataMatricesBSVAR presents the data matrices of dependent variables, Y, and regressors, X, for the homoskedastic bsvar model.

Public fields

Y: an NxT matrix of dependent variables, Y.
X: an KxT matrix of regressors, X.

Methods

Public methods

specify_data_matrices$new()
specify_data_matrices$get_data_matrices()
specify_data_matrices$clone()

Method `new()`

Create new data matrices DataMatricesBSVAR.

Usage

specify_data_matrices$new(data, p = 1L, exogenous = NULL)

Arguments

data: a (T+p)xN matrix with time series data.
p: a positive integer providing model's autoregressive lag order.
exogenous: a (T+p)xd matrix of exogenous variables. This matrix should not include a constant term.

Returns

New data matrices DataMatricesBSVAR.

Method `get_data_matrices()`

Returns the data matrices DataMatricesBSVAR as a list.

Usage

specify_data_matrices$get_data_matrices()

Examples

data(us_fiscal_lsuw)
YX = specify_data_matrices$new(data = us_fiscal_lsuw, p = 4)
YX$get_data_matrices()

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_data_matrices$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

data(us_fiscal_lsuw)
YX = specify_data_matrices$new(data = us_fiscal_lsuw, p = 4)
dim(YX$Y); dim(YX$X)


## ------------------------------------------------
## Method `specify_data_matrices$get_data_matrices`
## ------------------------------------------------

data(us_fiscal_lsuw)
YX = specify_data_matrices$new(data = us_fiscal_lsuw, p = 4)
YX$get_data_matrices()

R6 Class Representing IdentificationBSVARs

Description

The class IdentificationBSVARs presents the identifying restrictions for the bsvar models.

Public fields

VB: a list of N matrices determining the unrestricted elements of matrix B.

Methods

Public methods

specify_identification_bsvars$new()
specify_identification_bsvars$get_identification()
specify_identification_bsvars$set_identification()
specify_identification_bsvars$clone()

Method `new()`

Create new identifying restrictions IdentificationBSVARs.

Usage

specify_identification_bsvars$new(N, B)

Arguments

N: a positive integer - the number of dependent variables in the model.
B: a logical NxN matrix containing value TRUE for the elements of the structural matrix B to be estimated and value FALSE for exclusion restrictions to be set to zero.

Returns

Identifying restrictions IdentificationBSVARs.

Method `get_identification()`

Returns the elements of the identification pattern IdentificationBSVARs as a list.

Usage

specify_identification_bsvars$get_identification()

Examples

B    = matrix(c(TRUE,TRUE,TRUE,FALSE,FALSE,TRUE,FALSE,TRUE,TRUE), 3, 3); B
spec = specify_identification_bsvars$new(N = 3, B = B)
spec$get_identification()

Method `set_identification()`

Set new starting values StartingValuesBSVAR.

Usage

specify_identification_bsvars$set_identification(N, B)

Arguments

N: a positive integer - the number of dependent variables in the model.
B: a logical NxN matrix containing value TRUE for the elements of the structural matrix B to be estimated and value FALSE for exclusion restrictions to be set to zero.

Examples

spec = specify_identification_bsvars$new(N = 3) # specify a model with the default option
B    = matrix(c(TRUE,TRUE,TRUE,FALSE,FALSE,TRUE,FALSE,TRUE,TRUE), 3, 3); B
spec$set_identification(N = 3, B = B)  # modify an existing specification
spec$get_identification()              # check the outcome

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_identification_bsvars$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

specify_identification_bsvars$new(N = 3) # recursive specification for a 3-variable system

B = matrix(c(TRUE,TRUE,TRUE,FALSE,FALSE,TRUE,FALSE,TRUE,TRUE), 3, 3); B
specify_identification_bsvars$new(N = 3, B = B) # an alternative identification pattern


## ------------------------------------------------
## Method `specify_identification_bsvars$get_identification`
## ------------------------------------------------

B    = matrix(c(TRUE,TRUE,TRUE,FALSE,FALSE,TRUE,FALSE,TRUE,TRUE), 3, 3); B
spec = specify_identification_bsvars$new(N = 3, B = B)
spec$get_identification()


## ------------------------------------------------
## Method `specify_identification_bsvars$set_identification`
## ------------------------------------------------

spec = specify_identification_bsvars$new(N = 3) # specify a model with the default option
B    = matrix(c(TRUE,TRUE,TRUE,FALSE,FALSE,TRUE,FALSE,TRUE,TRUE), 3, 3); B
spec$set_identification(N = 3, B = B)  # modify an existing specification
spec$get_identification()              # check the outcome

R6 Class Representing PosteriorBSVAR

Description

The class PosteriorBSVAR contains posterior output and the specification including the last MCMC draw for the homoskedastic bsvar model. Note that due to the thinning of the MCMC output the starting value in element last_draw might not be equal to the last draw provided in element posterior.

Public fields

last_draw: an object of class BSVAR with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().
posterior: a list containing Bayesian estimation output collected in elements an NxNxS array B, an NxKxS array A, and a 5xS matrix hyper.

Methods

Public methods

specify_posterior_bsvar$new()
specify_posterior_bsvar$get_posterior()
specify_posterior_bsvar$get_last_draw()
specify_posterior_bsvar$is_normalised()
specify_posterior_bsvar$set_normalised()
specify_posterior_bsvar$clone()

Method `new()`

Create a new posterior output PosteriorBSVAR.

Usage

specify_posterior_bsvar$new(specification_bsvar, posterior_bsvar)

Arguments

specification_bsvar: an object of class BSVAR with the last draw of the current MCMC run as the starting value.
posterior_bsvar: a list containing Bayesian estimation output collected in elements an NxNxS array B, an NxKxS array A, and a 5xS matrix hyper.

Returns

A posterior output PosteriorBSVAR.

Method `get_posterior()`

Returns a list containing Bayesian estimation output collected in elements an NxNxS array B, an NxKxS array A, and a 5xS matrix hyper.

Usage

specify_posterior_bsvar$get_posterior()

Examples

data(us_fiscal_lsuw)
specification  = specify_bsvar$new(us_fiscal_lsuw)
set.seed(123)
estimate       = estimate(specification, 50)
estimate$get_posterior()

Method `get_last_draw()`

Returns an object of class BSVAR with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Usage

specify_posterior_bsvar$get_last_draw()

Examples

data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 4)
set.seed(123)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 10)

Method `is_normalised()`

Returns TRUE if the posterior has been normalised using normalise_posterior() and FALSE otherwise.

Usage

specify_posterior_bsvar$is_normalised()

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 4)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10, thin = 1)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag((-1) * sign(diag(BB))) %*% BB         # set negative diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()

Method `set_normalised()`

Sets the private indicator normalised to TRUE.

Usage

specify_posterior_bsvar$set_normalised(value)

Arguments

value: (optional) a logical value to be passed to indicator normalised.

Examples

# This is an internal function that is run while executing normalise_posterior()
# Observe its working by analysing the workflow:

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 4)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10, thin = 1)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag(sign(diag(BB))) %*% BB                # set positive diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_posterior_bsvar$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

# This is a function that is used within estimate()
data(us_fiscal_lsuw)
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 4)
set.seed(123)
estimate       = estimate(specification, 50)
class(estimate)


## ------------------------------------------------
## Method `specify_posterior_bsvar$get_posterior`
## ------------------------------------------------

data(us_fiscal_lsuw)
specification  = specify_bsvar$new(us_fiscal_lsuw)
set.seed(123)
estimate       = estimate(specification, 50)
estimate$get_posterior()


## ------------------------------------------------
## Method `specify_posterior_bsvar$get_last_draw`
## ------------------------------------------------

data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 4)
set.seed(123)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 10)


## ------------------------------------------------
## Method `specify_posterior_bsvar$is_normalised`
## ------------------------------------------------

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 4)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10, thin = 1)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag((-1) * sign(diag(BB))) %*% BB         # set negative diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()


## ------------------------------------------------
## Method `specify_posterior_bsvar$set_normalised`
## ------------------------------------------------

# This is an internal function that is run while executing normalise_posterior()
# Observe its working by analysing the workflow:

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 4)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10, thin = 1)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag(sign(diag(BB))) %*% BB                # set positive diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()

R6 Class Representing PosteriorBSVARMIX

Description

The class PosteriorBSVARMIX contains posterior output and the specification including the last MCMC draw for the bsvar model with a zero-mean mixture of normals model for structural shocks. Note that due to the thinning of the MCMC output the starting value in element last_draw might not be equal to the last draw provided in element posterior.

Public fields

last_draw: an object of class BSVARMIX with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().
posterior: a list containing Bayesian estimation output.

Methods

Public methods

specify_posterior_bsvar_mix$new()
specify_posterior_bsvar_mix$get_posterior()
specify_posterior_bsvar_mix$get_last_draw()
specify_posterior_bsvar_mix$is_normalised()
specify_posterior_bsvar_mix$set_normalised()
specify_posterior_bsvar_mix$clone()

Method `new()`

Create a new posterior output PosteriorBSVARMIX.

Usage

specify_posterior_bsvar_mix$new(specification_bsvar, posterior_bsvar)

Arguments

specification_bsvar: an object of class BSVARMIX with the last draw of the current MCMC run as the starting value.
posterior_bsvar: a list containing Bayesian estimation output.

Returns

A posterior output PosteriorBSVARMIX.

Method `get_posterior()`

Returns a list containing Bayesian estimation output.

Usage

specify_posterior_bsvar_mix$get_posterior()

Examples

data(us_fiscal_lsuw)
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, M = 2)
set.seed(123)
estimate       = estimate(specification, 10, thin = 1)
estimate$get_posterior()

Method `get_last_draw()`

Returns an object of class BSVARMIX with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Usage

specify_posterior_bsvar_mix$get_last_draw()

Examples

data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 4, M = 2)

# run the burn-in
set.seed(123)
burn_in        = estimate(specification, 10, thin = 2)

# estimate the model
posterior      = estimate(burn_in, 10, thin = 2)

Method `is_normalised()`

Returns TRUE if the posterior has been normalised using normalise_posterior() and FALSE otherwise.

Usage

specify_posterior_bsvar_mix$is_normalised()

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 4, M = 2)

# estimate the model
set.seed(123)
posterior      = estimate(specification, 10, thin = 1)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag((-1) * sign(diag(BB))) %*% BB         # set negative diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()

Method `set_normalised()`

Sets the private indicator normalised to TRUE.

Usage

specify_posterior_bsvar_mix$set_normalised(value)

Arguments

value: (optional) a logical value to be passed to indicator normalised.

Examples

# This is an internal function that is run while executing normalise_posterior()
# Observe its working by analysing the workflow:

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 4, M = 2)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10, thin = 1)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag(sign(diag(BB))) %*% BB                # set positive diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_posterior_bsvar_mix$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

# This is a function that is used within estimate()
data(us_fiscal_lsuw)
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 4, M = 2)
set.seed(123)
estimate       = estimate(specification, 10, thin = 1)
class(estimate)


## ------------------------------------------------
## Method `specify_posterior_bsvar_mix$get_posterior`
## ------------------------------------------------

data(us_fiscal_lsuw)
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, M = 2)
set.seed(123)
estimate       = estimate(specification, 10, thin = 1)
estimate$get_posterior()


## ------------------------------------------------
## Method `specify_posterior_bsvar_mix$get_last_draw`
## ------------------------------------------------

data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 4, M = 2)

# run the burn-in
set.seed(123)
burn_in        = estimate(specification, 10, thin = 2)

# estimate the model
posterior      = estimate(burn_in, 10, thin = 2)


## ------------------------------------------------
## Method `specify_posterior_bsvar_mix$is_normalised`
## ------------------------------------------------

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 4, M = 2)

# estimate the model
set.seed(123)
posterior      = estimate(specification, 10, thin = 1)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag((-1) * sign(diag(BB))) %*% BB         # set negative diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()


## ------------------------------------------------
## Method `specify_posterior_bsvar_mix$set_normalised`
## ------------------------------------------------

# This is an internal function that is run while executing normalise_posterior()
# Observe its working by analysing the workflow:

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 4, M = 2)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10, thin = 1)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag(sign(diag(BB))) %*% BB                # set positive diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()

R6 Class Representing PosteriorBSVARMSH

Description

The class PosteriorBSVARMSH contains posterior output and the specification including the last MCMC draw for the bsvar model with Markov Switching Heteroskedasticity. Note that due to the thinning of the MCMC output the starting value in element last_draw might not be equal to the last draw provided in element posterior.

Public fields

last_draw: an object of class BSVARMSH with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().
posterior: a list containing Bayesian estimation output.

Methods

Public methods

specify_posterior_bsvar_msh$new()
specify_posterior_bsvar_msh$get_posterior()
specify_posterior_bsvar_msh$get_last_draw()
specify_posterior_bsvar_msh$is_normalised()
specify_posterior_bsvar_msh$set_normalised()
specify_posterior_bsvar_msh$clone()

Method `new()`

Create a new posterior output PosteriorBSVARMSH.

Usage

specify_posterior_bsvar_msh$new(specification_bsvar, posterior_bsvar)

Arguments

specification_bsvar: an object of class BSVARMSH with the last draw of the current MCMC run as the starting value.
posterior_bsvar: a list containing Bayesian estimation output.

Returns

A posterior output PosteriorBSVARMSH.

Method `get_posterior()`

Returns a list containing Bayesian estimation output.

Usage

specify_posterior_bsvar_msh$get_posterior()

Examples

data(us_fiscal_lsuw)
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, M = 2)
set.seed(123)
estimate       = estimate(specification, 10, thin = 1)
estimate$get_posterior()

Method `get_last_draw()`

Returns an object of class BSVARMSH with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Usage

specify_posterior_bsvar_msh$get_last_draw()

Examples

data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 4, M = 2)

# run the burn-in
set.seed(123)
burn_in        = estimate(specification, 10, thin = 2)

# estimate the model
posterior      = estimate(burn_in, 10, thin = 2)

Method `is_normalised()`

Returns TRUE if the posterior has been normalised using normalise_posterior() and FALSE otherwise.

Usage

specify_posterior_bsvar_msh$is_normalised()

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 4, M = 2)

# estimate the model
set.seed(123)
posterior      = estimate(specification, 10, thin = 1)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag((-1) * sign(diag(BB))) %*% BB         # set negative diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()

Method `set_normalised()`

Sets the private indicator normalised to TRUE.

Usage

specify_posterior_bsvar_msh$set_normalised(value)

Arguments

value: (optional) a logical value to be passed to indicator normalised.

Examples

# This is an internal function that is run while executing normalise_posterior()
# Observe its working by analysing the workflow:

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 4, M = 2)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10, thin = 1)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag(sign(diag(BB))) %*% BB                # set positive diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_posterior_bsvar_msh$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

# This is a function that is used within estimate()
data(us_fiscal_lsuw)
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 4, M = 2)
set.seed(123)
estimate       = estimate(specification, 10, thin = 1)
class(estimate)


## ------------------------------------------------
## Method `specify_posterior_bsvar_msh$get_posterior`
## ------------------------------------------------

data(us_fiscal_lsuw)
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, M = 2)
set.seed(123)
estimate       = estimate(specification, 10, thin = 1)
estimate$get_posterior()


## ------------------------------------------------
## Method `specify_posterior_bsvar_msh$get_last_draw`
## ------------------------------------------------

data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 4, M = 2)

# run the burn-in
set.seed(123)
burn_in        = estimate(specification, 10, thin = 2)

# estimate the model
posterior      = estimate(burn_in, 10, thin = 2)


## ------------------------------------------------
## Method `specify_posterior_bsvar_msh$is_normalised`
## ------------------------------------------------

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 4, M = 2)

# estimate the model
set.seed(123)
posterior      = estimate(specification, 10, thin = 1)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag((-1) * sign(diag(BB))) %*% BB         # set negative diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()


## ------------------------------------------------
## Method `specify_posterior_bsvar_msh$set_normalised`
## ------------------------------------------------

# This is an internal function that is run while executing normalise_posterior()
# Observe its working by analysing the workflow:

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 4, M = 2)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10, thin = 1)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag(sign(diag(BB))) %*% BB                # set positive diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()

R6 Class Representing PosteriorBSVARSV

Description

The class PosteriorBSVARSV contains posterior output and the specification including the last MCMC draw for the bsvar model with Stochastic Volatility heteroskedasticity. Note that due to the thinning of the MCMC output the starting value in element last_draw might not be equal to the last draw provided in element posterior.

Public fields

last_draw: an object of class BSVARSV with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().
posterior: a list containing Bayesian estimation output.

Methods

Public methods

specify_posterior_bsvar_sv$new()
specify_posterior_bsvar_sv$get_posterior()
specify_posterior_bsvar_sv$get_last_draw()
specify_posterior_bsvar_sv$is_normalised()
specify_posterior_bsvar_sv$set_normalised()
specify_posterior_bsvar_sv$clone()

Method `new()`

Create a new posterior output PosteriorBSVARSV.

Usage

specify_posterior_bsvar_sv$new(specification_bsvar, posterior_bsvar)

Arguments

specification_bsvar: an object of class BSVARSV with the last draw of the current MCMC run as the starting value.
posterior_bsvar: a list containing Bayesian estimation output.

Returns

A posterior output PosteriorBSVARSV.

Method `get_posterior()`

Returns a list containing Bayesian estimation.

Usage

specify_posterior_bsvar_sv$get_posterior()

Examples

data(us_fiscal_lsuw)
specification  = specify_bsvar_sv$new(us_fiscal_lsuw)
set.seed(123)
estimate       = estimate(specification, 5, thin = 1)
estimate$get_posterior()

Method `get_last_draw()`

Returns an object of class BSVARSV with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Usage

specify_posterior_bsvar_sv$get_last_draw()

Examples

data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 4)
set.seed(123)

# run the burn-in
burn_in        = estimate(specification, 5, thin = 1)

# estimate the model
posterior      = estimate(burn_in, 5, thin = 1)

Method `is_normalised()`

Returns TRUE if the posterior has been normalised using normalise_posterior() and FALSE otherwise.

Usage

specify_posterior_bsvar_sv$is_normalised()

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 4)

# estimate the model
set.seed(123)
posterior      = estimate(specification, 5, thin = 1)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag((-1) * sign(diag(BB))) %*% BB         # set negative diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()

Method `set_normalised()`

Sets the private indicator normalised to TRUE.

Usage

specify_posterior_bsvar_sv$set_normalised(value)

Arguments

value: (optional) a logical value to be passed to indicator normalised.

Examples

# This is an internal function that is run while executing normalise_posterior()
# Observe its working by analysing the workflow:

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 4)

# estimate the model
set.seed(123)
posterior      = estimate(specification, 5, thin = 1)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag(sign(diag(BB))) %*% BB                # set positive diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_posterior_bsvar_sv$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

# This is a function that is used within estimate()
data(us_fiscal_lsuw)
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 4)
set.seed(123)
estimate       = estimate(specification, 5, thin = 1)
class(estimate)


## ------------------------------------------------
## Method `specify_posterior_bsvar_sv$get_posterior`
## ------------------------------------------------

data(us_fiscal_lsuw)
specification  = specify_bsvar_sv$new(us_fiscal_lsuw)
set.seed(123)
estimate       = estimate(specification, 5, thin = 1)
estimate$get_posterior()


## ------------------------------------------------
## Method `specify_posterior_bsvar_sv$get_last_draw`
## ------------------------------------------------

data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 4)
set.seed(123)

# run the burn-in
burn_in        = estimate(specification, 5, thin = 1)

# estimate the model
posterior      = estimate(burn_in, 5, thin = 1)


## ------------------------------------------------
## Method `specify_posterior_bsvar_sv$is_normalised`
## ------------------------------------------------

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 4)

# estimate the model
set.seed(123)
posterior      = estimate(specification, 5, thin = 1)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag((-1) * sign(diag(BB))) %*% BB         # set negative diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()


## ------------------------------------------------
## Method `specify_posterior_bsvar_sv$set_normalised`
## ------------------------------------------------

# This is an internal function that is run while executing normalise_posterior()
# Observe its working by analysing the workflow:

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 4)

# estimate the model
set.seed(123)
posterior      = estimate(specification, 5, thin = 1)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag(sign(diag(BB))) %*% BB                # set positive diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()

R6 Class Representing PosteriorBSVART

Description

The class PosteriorBSVART contains posterior output and the specification including the last MCMC draw for the bsvar model with t-distributed structural shocks. Note that due to the thinning of the MCMC output the starting value in element last_draw might not be equal to the last draw provided in element posterior.

Public fields

last_draw: an object of class BSVART with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().
posterior: a list containing Bayesian estimation output.

Methods

Public methods

specify_posterior_bsvar_t$new()
specify_posterior_bsvar_t$get_posterior()
specify_posterior_bsvar_t$get_last_draw()
specify_posterior_bsvar_t$is_normalised()
specify_posterior_bsvar_t$set_normalised()
specify_posterior_bsvar_t$clone()

Method `new()`

Create a new posterior output PosteriorBSVART.

Usage

specify_posterior_bsvar_t$new(specification_bsvar, posterior_bsvar)

Arguments

specification_bsvar: an object of class BSVART with the last draw of the current MCMC run as the starting value.
posterior_bsvar: a list containing Bayesian estimation output.

Returns

A posterior output PosteriorBSVART.

Method `get_posterior()`

Returns a list containing Bayesian estimation output.

Usage

specify_posterior_bsvar_t$get_posterior()

Examples

data(us_fiscal_lsuw)
specification  = specify_bsvar_t$new(us_fiscal_lsuw)
set.seed(123)
estimate       = estimate(specification, 10)
estimate$get_posterior()

Method `get_last_draw()`

Returns an object of class BSVART with the last draw of the current MCMC run as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Usage

specify_posterior_bsvar_t$get_last_draw()

Examples

data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_t$new(us_fiscal_lsuw, p = 4)

# run the burn-in
set.seed(123)
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 10)

Method `is_normalised()`

Returns TRUE if the posterior has been normalised using normalise_posterior() and FALSE otherwise.

Usage

specify_posterior_bsvar_t$is_normalised()

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_t$new(us_fiscal_lsuw, p = 4)

# estimate the model
set.seed(123)
posterior      = estimate(specification, 10)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag((-1) * sign(diag(BB))) %*% BB         # set negative diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()

Method `set_normalised()`

Sets the private indicator normalised to TRUE.

Usage

specify_posterior_bsvar_t$set_normalised(value)

Arguments

value: (optional) a logical value to be passed to indicator normalised.

Examples

# This is an internal function that is run while executing normalise_posterior()
# Observe its working by analysing the workflow:

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_t$new(us_fiscal_lsuw, p = 4)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag(sign(diag(BB))) %*% BB                # set positive diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_posterior_bsvar_t$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

# This is a function that is used within estimate()
data(us_fiscal_lsuw)
specification  = specify_bsvar_t$new(us_fiscal_lsuw, p = 4)
set.seed(123)
estimate       = estimate(specification, 10)
class(estimate)


## ------------------------------------------------
## Method `specify_posterior_bsvar_t$get_posterior`
## ------------------------------------------------

data(us_fiscal_lsuw)
specification  = specify_bsvar_t$new(us_fiscal_lsuw)
set.seed(123)
estimate       = estimate(specification, 10)
estimate$get_posterior()


## ------------------------------------------------
## Method `specify_posterior_bsvar_t$get_last_draw`
## ------------------------------------------------

data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_t$new(us_fiscal_lsuw, p = 4)

# run the burn-in
set.seed(123)
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 10)


## ------------------------------------------------
## Method `specify_posterior_bsvar_t$is_normalised`
## ------------------------------------------------

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_t$new(us_fiscal_lsuw, p = 4)

# estimate the model
set.seed(123)
posterior      = estimate(specification, 10)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag((-1) * sign(diag(BB))) %*% BB         # set negative diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()


## ------------------------------------------------
## Method `specify_posterior_bsvar_t$set_normalised`
## ------------------------------------------------

# This is an internal function that is run while executing normalise_posterior()
# Observe its working by analysing the workflow:

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_t$new(us_fiscal_lsuw, p = 4)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# check normalisation status beforehand
posterior$is_normalised()

# normalise the posterior
BB            = posterior$last_draw$starting_values$B      # get the last draw of B
B_hat         = diag(sign(diag(BB))) %*% BB                # set positive diagonal elements
normalise_posterior(posterior, B_hat)                      # draws in posterior are normalised

# check normalisation status afterwards
posterior$is_normalised()

R6 Class Representing PriorBSVAR

Description

The class PriorBSVAR presents a prior specification for the homoskedastic bsvar model.

Public fields

A: an NxK matrix, the mean of the normal prior distribution for the parameter matrix A.
A_V_inv: a KxK precision matrix of the normal prior distribution for each of the row of the parameter matrix A. This precision matrix is equation invariant.
B_V_inv: an NxN precision matrix of the generalised-normal prior distribution for the structural matrix B. This precision matrix is equation invariant.
B_nu: a positive integer greater of equal than N, a shape parameter of the generalised-normal prior distribution for the structural matrix B.
hyper_nu_B: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the overall shrinkage parameter for matrix B.
hyper_a_B: a positive scalar, the shape parameter of the gamma prior for the second-level hierarchy for the overall shrinkage parameter for matrix B.
hyper_s_BB: a positive scalar, the scale parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix B.
hyper_nu_BB: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix B.
hyper_nu_A: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the overall shrinkage parameter for matrix A.
hyper_a_A: a positive scalar, the shape parameter of the gamma prior for the second-level hierarchy for the overall shrinkage parameter for matrix A.
hyper_s_AA: a positive scalar, the scale parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix A.
hyper_nu_AA: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix A.

Methods

Public methods

specify_prior_bsvar$new()
specify_prior_bsvar$get_prior()
specify_prior_bsvar$clone()

Method `new()`

Create a new prior specification PriorBSVAR.

Usage

specify_prior_bsvar$new(N, p, d = 0, stationary = rep(FALSE, N))

Arguments

N: a positive integer - the number of dependent variables in the model.
p: a positive integer - the autoregressive lag order of the SVAR model.
d: a positive integer - the number of exogenous variables in the model.
stationary: an N logical vector - its element set to FALSE sets the prior mean for the autoregressive parameters of the Nth equation to the white noise process, otherwise to random walk.

Returns

A new prior specification PriorBSVAR.

Examples

# a prior for 3-variable example with one lag and stationary data
prior = specify_prior_bsvar$new(N = 3, p = 1, stationary = rep(TRUE, 3))
prior$A # show autoregressive prior mean

Method `get_prior()`

Returns the elements of the prior specification PriorBSVAR as a list.

Usage

specify_prior_bsvar$get_prior()

Examples

# a prior for 3-variable example with four lags
prior = specify_prior_bsvar$new(N = 3, p = 4)
prior$get_prior() # show the prior as list

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_prior_bsvar$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

prior = specify_prior_bsvar$new(N = 3, p = 1)  # a prior for 3-variable example with one lag
prior$A                                        # show autoregressive prior mean


## ------------------------------------------------
## Method `specify_prior_bsvar$new`
## ------------------------------------------------

# a prior for 3-variable example with one lag and stationary data
prior = specify_prior_bsvar$new(N = 3, p = 1, stationary = rep(TRUE, 3))
prior$A # show autoregressive prior mean


## ------------------------------------------------
## Method `specify_prior_bsvar$get_prior`
## ------------------------------------------------

# a prior for 3-variable example with four lags
prior = specify_prior_bsvar$new(N = 3, p = 4)
prior$get_prior() # show the prior as list

R6 Class Representing PriorBSVARMIX

Description

The class PriorBSVARMIX presents a prior specification for the bsvar model with a zero-mean mixture of normals model for structural shocks.

Super classes

bsvars::PriorBSVAR -> bsvars::PriorBSVARMSH -> PriorBSVARMIX

Public fields

A: an NxK matrix, the mean of the normal prior distribution for the parameter matrix A.
A_V_inv: a KxK precision matrix of the normal prior distribution for each of the row of the parameter matrix A. This precision matrix is equation invariant.
B_V_inv: an NxN precision matrix of the generalised-normal prior distribution for the structural matrix B. This precision matrix is equation invariant.
B_nu: a positive integer greater of equal than N, a shape parameter of the generalised-normal prior distribution for the structural matrix B.
hyper_nu_B: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the overall shrinkage parameter for matrix B.
hyper_a_B: a positive scalar, the shape parameter of the gamma prior for the second-level hierarchy for the overall shrinkage parameter for matrix B.
hyper_s_BB: a positive scalar, the scale parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix B.
hyper_nu_BB: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix B.
hyper_nu_A: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the overall shrinkage parameter for matrix A.
hyper_a_A: a positive scalar, the shape parameter of the gamma prior for the second-level hierarchy for the overall shrinkage parameter for matrix A.
hyper_s_AA: a positive scalar, the scale parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix A.
hyper_nu_AA: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix A.
sigma_nu: a positive scalar, the shape parameter of the inverted-gamma 2 for mixture component-dependent variances of the structural shocks, \sigma^2_{n.s_t}.
sigma_s: a positive scalar, the scale parameter of the inverted-gamma 2 for mixture component-dependent variances of the structural shocks, \sigma^2_{n.s_t}.
PR_TR: an MxM matrix, the matrix of hyper-parameters of the row-specific Dirichlet prior distribution for the state probabilities the Markov process s_t. Its rows must be identical.

Methods

Public methods

specify_prior_bsvar_mix$clone()

Inherited methods

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_prior_bsvar_mix$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

prior = specify_prior_bsvar_mix$new(N = 3, p = 1, M = 2)  # specify the prior
prior$A                                        # show autoregressive prior mean

R6 Class Representing PriorBSVARMSH

Description

The class PriorBSVARMSH presents a prior specification for the bsvar model with Markov Switching Heteroskedasticity.

Super class

bsvars::PriorBSVAR -> PriorBSVARMSH

Public fields

A: an NxK matrix, the mean of the normal prior distribution for the parameter matrix A.
A_V_inv: a KxK precision matrix of the normal prior distribution for each of the row of the parameter matrix A. This precision matrix is equation invariant.
B_V_inv: an NxN precision matrix of the generalised-normal prior distribution for the structural matrix B. This precision matrix is equation invariant.
B_nu: a positive integer greater of equal than N, a shape parameter of the generalised-normal prior distribution for the structural matrix B.
hyper_nu_B: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the overall shrinkage parameter for matrix B.
hyper_a_B: a positive scalar, the shape parameter of the gamma prior for the second-level hierarchy for the overall shrinkage parameter for matrix B.
hyper_s_BB: a positive scalar, the scale parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix B.
hyper_nu_BB: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix B.
hyper_nu_A: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the overall shrinkage parameter for matrix A.
hyper_a_A: a positive scalar, the shape parameter of the gamma prior for the second-level hierarchy for the overall shrinkage parameter for matrix A.
hyper_s_AA: a positive scalar, the scale parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix A.
hyper_nu_AA: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix A.
sigma_nu: a positive scalar, the shape parameter of the inverted-gamma 2 for MS state-dependent variances of the structural shocks, \sigma^2_{n.s_t}.
sigma_s: a positive scalar, the scale parameter of the inverted-gamma 2 for MS state-dependent variances of the structural shocks, \sigma^2_{n.s_t}.
PR_TR: an MxM matrix, the matrix of hyper-parameters of the row-specific Dirichlet prior distribution for transition probabilities matrix P of the Markov process s_t.

Methods

Public methods

specify_prior_bsvar_msh$new()
specify_prior_bsvar_msh$get_prior()
specify_prior_bsvar_msh$clone()

Method `new()`

Create a new prior specification PriorBSVARMSH.

Usage

specify_prior_bsvar_msh$new(N, p, d = 0, M, stationary = rep(FALSE, N))

Arguments

N: a positive integer - the number of dependent variables in the model.
p: a positive integer - the autoregressive lag order of the SVAR model.
d: a positive integer - the number of exogenous variables in the model.
M: an integer greater than 1 - the number of Markov process' heteroskedastic regimes.
stationary: an N logical vector - its element set to FALSE sets the prior mean for the autoregressive parameters of the Nth equation to the white noise process, otherwise to random walk.

Returns

A new prior specification PriorBSVARMSH.

Method `get_prior()`

Returns the elements of the prior specification PriorBSVARMSH as a list.

Usage

specify_prior_bsvar_msh$get_prior()

Examples

# a prior for 3-variable example with four lags and two regimes
prior = specify_prior_bsvar_msh$new(N = 3, p = 4, M = 2)
prior$get_prior() # show the prior as list

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_prior_bsvar_msh$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

prior = specify_prior_bsvar_msh$new(N = 3, p = 1, M = 2)  # specify the prior
prior$A                                        # show autoregressive prior mean


## ------------------------------------------------
## Method `specify_prior_bsvar_msh$get_prior`
## ------------------------------------------------

# a prior for 3-variable example with four lags and two regimes
prior = specify_prior_bsvar_msh$new(N = 3, p = 4, M = 2)
prior$get_prior() # show the prior as list

R6 Class Representing PriorBSVARSV

Description

The class PriorBSVARSV presents a prior specification for the bsvar model with Stochastic Volatility heteroskedasticity.

Super class

bsvars::PriorBSVAR -> PriorBSVARSV

Public fields

A: an NxK matrix, the mean of the normal prior distribution for the parameter matrix A.
A_V_inv: a KxK precision matrix of the normal prior distribution for each of the row of the parameter matrix A. This precision matrix is equation invariant.
B_V_inv: an NxN precision matrix of the generalised-normal prior distribution for the structural matrix B. This precision matrix is equation invariant.
B_nu: a positive integer greater of equal than N, a shape parameter of the generalised-normal prior distribution for the structural matrix B.
hyper_nu_B: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the overall shrinkage parameter for matrix B.
hyper_a_B: a positive scalar, the shape parameter of the gamma prior for the second-level hierarchy for the overall shrinkage parameter for matrix B.
hyper_s_BB: a positive scalar, the scale parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix B.
hyper_nu_BB: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix B.
hyper_nu_A: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the overall shrinkage parameter for matrix A.
hyper_a_A: a positive scalar, the shape parameter of the gamma prior for the second-level hierarchy for the overall shrinkage parameter for matrix A.
hyper_s_AA: a positive scalar, the scale parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix A.
hyper_nu_AA: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix A.
sv_a_: a positive scalar, the shape parameter of the gamma prior in the hierarchical prior for \sigma^2_{\omega}.
sv_s_: a positive scalar, the scale parameter of the gamma prior in the hierarchical prior for \sigma^2_{\omega}.

Methods

Public methods

specify_prior_bsvar_sv$new()
specify_prior_bsvar_sv$get_prior()
specify_prior_bsvar_sv$clone()

Method `new()`

Create a new prior specification PriorBSVARSV.

Usage

specify_prior_bsvar_sv$new(N, p, d = 0, stationary = rep(FALSE, N))

Arguments

N: a positive integer - the number of dependent variables in the model.
p: a positive integer - the autoregressive lag order of the SVAR model.
d: a positive integer - the number of exogenous variables in the model.
stationary: an N logical vector - its element set to FALSE sets the prior mean for the autoregressive parameters of the Nth equation to the white noise process, otherwise to random walk.

Returns

A new prior specification PriorBSVARSV.

Method `get_prior()`

Returns the elements of the prior specification PriorBSVARSV as a list.

Usage

specify_prior_bsvar_sv$get_prior()

Examples

# a prior for 3-variable example with four lags
prior = specify_prior_bsvar_sv$new(N = 3, p = 4)
prior$get_prior() # show the prior as list

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_prior_bsvar_sv$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

prior = specify_prior_bsvar_sv$new(N = 3, p = 1) # a prior for 3-variable example with one lag
prior$A                                          # show autoregressive prior mean


## ------------------------------------------------
## Method `specify_prior_bsvar_sv$get_prior`
## ------------------------------------------------

# a prior for 3-variable example with four lags
prior = specify_prior_bsvar_sv$new(N = 3, p = 4)
prior$get_prior() # show the prior as list

R6 Class Representing PriorBSVART

Description

The class PriorBSVART presents a prior specification for the bsvar model with t-distributed structural shocks.

Super class

bsvars::PriorBSVAR -> PriorBSVART

Public fields

A: an NxK matrix, the mean of the normal prior distribution for the parameter matrix A.
A_V_inv: a KxK precision matrix of the normal prior distribution for each of the row of the parameter matrix A. This precision matrix is equation invariant.
B_V_inv: an NxN precision matrix of the generalised-normal prior distribution for the structural matrix B. This precision matrix is equation invariant.
B_nu: a positive integer greater of equal than N, a shape parameter of the generalised-normal prior distribution for the structural matrix B.
hyper_nu_B: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the overall shrinkage parameter for matrix B.
hyper_a_B: a positive scalar, the shape parameter of the gamma prior for the second-level hierarchy for the overall shrinkage parameter for matrix B.
hyper_s_BB: a positive scalar, the scale parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix B.
hyper_nu_BB: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix B.
hyper_nu_A: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the overall shrinkage parameter for matrix A.
hyper_a_A: a positive scalar, the shape parameter of the gamma prior for the second-level hierarchy for the overall shrinkage parameter for matrix A.
hyper_s_AA: a positive scalar, the scale parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix A.
hyper_nu_AA: a positive scalar, the shape parameter of the inverted-gamma 2 prior for the third-level of hierarchy for overall shrinkage parameter for matrix A.

Methods

Public methods

specify_prior_bsvar_t$clone()

Inherited methods

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_prior_bsvar_t$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

prior = specify_prior_bsvar_t$new(N = 3, p = 1)  # specify the prior
prior$A                                        # show autoregressive prior mean

R6 Class Representing StartingValuesBSVAR

Description

The class StartingValuesBSVAR presents starting values for the homoskedastic bsvar model.

Public fields

A: an NxK matrix of starting values for the parameter A.
B: an NxN matrix of starting values for the parameter B.
hyper: a (2*N+1)x2 matrix of starting values for the shrinkage hyper-parameters of the hierarchical prior distribution.

Methods

Public methods

specify_starting_values_bsvar$new()
specify_starting_values_bsvar$get_starting_values()
specify_starting_values_bsvar$set_starting_values()
specify_starting_values_bsvar$clone()

Method `new()`

Create new starting values StartingValuesBSVAR.

Usage

specify_starting_values_bsvar$new(N, p, d = 0)

Arguments

N: a positive integer - the number of dependent variables in the model.
p: a positive integer - the autoregressive lag order of the SVAR model.
d: a positive integer - the number of exogenous variables in the model.

Returns

Starting values StartingValuesBSVAR.

Examples

# starting values for a homoskedastic bsvar with 4 lags for a 3-variable system
sv = specify_starting_values_bsvar$new(N = 3, p = 4)

Method `get_starting_values()`

Returns the elements of the starting values StartingValuesBSVAR as a list.

Usage

specify_starting_values_bsvar$get_starting_values()

Examples

# starting values for a homoskedastic bsvar with 1 lag for a 3-variable system
sv = specify_starting_values_bsvar$new(N = 3, p = 1)
sv$get_starting_values()   # show starting values as list

Method `set_starting_values()`

Returns the elements of the starting values StartingValuesBSVAR as a list.

Usage

specify_starting_values_bsvar$set_starting_values(last_draw)

Arguments

last_draw: a list containing the last draw of elements B - an NxN matrix, A - an NxK matrix, and hyper - a vector of 5 positive real numbers.

Returns

An object of class StartingValuesBSVAR including the last draw of the current MCMC as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Examples

# starting values for a homoskedastic bsvar with 1 lag for a 3-variable system
sv = specify_starting_values_bsvar$new(N = 3, p = 1)

# Modify the starting values by:
sv_list = sv$get_starting_values()   # getting them as list
sv_list$A <- matrix(rnorm(12), 3, 4) # modifying the entry
sv$set_starting_values(sv_list)      # providing to the class object

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_starting_values_bsvar$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

# starting values for a homoskedastic bsvar for a 3-variable system
sv = specify_starting_values_bsvar$new(N = 3, p = 1)


## ------------------------------------------------
## Method `specify_starting_values_bsvar$new`
## ------------------------------------------------

# starting values for a homoskedastic bsvar with 4 lags for a 3-variable system
sv = specify_starting_values_bsvar$new(N = 3, p = 4)


## ------------------------------------------------
## Method `specify_starting_values_bsvar$get_starting_values`
## ------------------------------------------------

# starting values for a homoskedastic bsvar with 1 lag for a 3-variable system
sv = specify_starting_values_bsvar$new(N = 3, p = 1)
sv$get_starting_values()   # show starting values as list


## ------------------------------------------------
## Method `specify_starting_values_bsvar$set_starting_values`
## ------------------------------------------------

# starting values for a homoskedastic bsvar with 1 lag for a 3-variable system
sv = specify_starting_values_bsvar$new(N = 3, p = 1)

# Modify the starting values by:
sv_list = sv$get_starting_values()   # getting them as list
sv_list$A <- matrix(rnorm(12), 3, 4) # modifying the entry
sv$set_starting_values(sv_list)      # providing to the class object

R6 Class Representing StartingValuesBSVARMIX

Description

The class StartingValuesBSVARMIX presents starting values for the bsvar model with a zero-mean mixture of normals model for structural shocks.

Super classes

bsvars::StartingValuesBSVAR -> bsvars::StartingValuesBSVARMSH -> StartingValuesBSVARMIX

Public fields

A: an NxK matrix of starting values for the parameter A.
B: an NxN matrix of starting values for the parameter B.
hyper: a (2*N+1)x2 matrix of starting values for the shrinkage hyper-parameters of the hierarchical prior distribution.
sigma2: an NxM matrix of starting values for the MS state-specific variances of the structural shocks. Its elements sum to value M over the rows.
PR_TR: an MxM matrix of starting values for the probability matrix of the Markov process. Its rows must be identical and the elements of each row sum to 1 over the rows.
xi: an MxT matrix of starting values for the Markov process indicator. Its columns are a chosen column of an identity matrix of order M.
pi_0: an M-vector of starting values for mixture components state probabilities. Its elements sum to 1.

Methods

Public methods

specify_starting_values_bsvar_mix$new()
specify_starting_values_bsvar_mix$clone()

Inherited methods

Method `new()`

Create new starting values StartingValuesBSVARMIX.

Usage

specify_starting_values_bsvar_mix$new(N, p, M, T, d = 0, finiteM = TRUE)

Arguments

N: a positive integer - the number of dependent variables in the model.
p: a positive integer - the autoregressive lag order of the SVAR model.
M: an integer greater than 1 - the number of components of the mixture of normals.
T: a positive integer - the the time series dimension of the dependent variable matrix Y.
d: a positive integer - the number of exogenous variables in the model.
finiteM: a logical value - if true a finite mixture model is estimated. Otherwise, a sparse mixture model is estimated in which M=20 and the number of visited states is estimated.

Returns

Starting values StartingValuesBSVARMIX.

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_starting_values_bsvar_mix$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

# starting values for a bsvar model for a 3-variable system
sv = specify_starting_values_bsvar_mix$new(N = 3, p = 1, M = 2, T = 100)

R6 Class Representing StartingValuesBSVARMSH

Description

The class StartingValuesBSVARMSH presents starting values for the bsvar model with Markov Switching Heteroskedasticity.

Super class

bsvars::StartingValuesBSVAR -> StartingValuesBSVARMSH

Public fields

A: an NxK matrix of starting values for the parameter A.
B: an NxN matrix of starting values for the parameter B.
hyper: a (2*N+1)x2 matrix of starting values for the shrinkage hyper-parameters of the hierarchical prior distribution.
sigma2: an NxM matrix of starting values for the MS state-specific variances of the structural shocks. Its elements sum to value M over the rows.
PR_TR: an MxM matrix of starting values for the transition probability matrix of the Markov process. Its elements sum to 1 over the rows.
xi: an MxT matrix of starting values for the Markov process indicator. Its columns are a chosen column of an identity matrix of order M.
pi_0: an M-vector of starting values for state probability at time t=0. Its elements sum to 1.

Methods

Public methods

specify_starting_values_bsvar_msh$new()
specify_starting_values_bsvar_msh$get_starting_values()
specify_starting_values_bsvar_msh$set_starting_values()
specify_starting_values_bsvar_msh$clone()

Method `new()`

Create new starting values StartingValuesBSVAR-MS.

Usage

specify_starting_values_bsvar_msh$new(N, p, M, T, d = 0, finiteM = TRUE)

Arguments

N: a positive integer - the number of dependent variables in the model.
p: a positive integer - the autoregressive lag order of the SVAR model.
M: an integer greater than 1 - the number of Markov process' heteroskedastic regimes.
T: a positive integer - the the time series dimension of the dependent variable matrix Y.
d: a positive integer - the number of exogenous variables in the model.
finiteM: a logical value - if true a stationary Markov switching model is estimated. Otherwise, a sparse Markov switching model is estimated in which M=20 and the number of visited states is estimated.

Returns

Starting values StartingValuesBSVAR-MS.

Method `get_starting_values()`

Returns the elements of the starting values StartingValuesBSVAR-MS as a list.

Usage

specify_starting_values_bsvar_msh$get_starting_values()

Examples

# starting values for a homoskedastic bsvar with 1 lag for a 3-variable system
sv = specify_starting_values_bsvar_msh$new(N = 3, p = 1, M = 2, T = 100)
sv$get_starting_values()   # show starting values as list

Method `set_starting_values()`

Returns the elements of the starting values StartingValuesBSVARMSH as a list.

Usage

specify_starting_values_bsvar_msh$set_starting_values(last_draw)

Arguments

last_draw: a list containing the last draw.

Returns

An object of class StartingValuesBSVAR-MS including the last draw of the current MCMC as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Examples

# starting values for a bsvar model with 1 lag for a 3-variable system
sv = specify_starting_values_bsvar_msh$new(N = 3, p = 1, M = 2, T = 100)

# Modify the starting values by:
sv_list = sv$get_starting_values()   # getting them as list
sv_list$A <- matrix(rnorm(12), 3, 4) # modifying the entry
sv$set_starting_values(sv_list)      # providing to the class object

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_starting_values_bsvar_msh$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

# starting values for a bsvar model for a 3-variable system
sv = specify_starting_values_bsvar_msh$new(N = 3, p = 1, M = 2, T = 100)


## ------------------------------------------------
## Method `specify_starting_values_bsvar_msh$get_starting_values`
## ------------------------------------------------

# starting values for a homoskedastic bsvar with 1 lag for a 3-variable system
sv = specify_starting_values_bsvar_msh$new(N = 3, p = 1, M = 2, T = 100)
sv$get_starting_values()   # show starting values as list


## ------------------------------------------------
## Method `specify_starting_values_bsvar_msh$set_starting_values`
## ------------------------------------------------

# starting values for a bsvar model with 1 lag for a 3-variable system
sv = specify_starting_values_bsvar_msh$new(N = 3, p = 1, M = 2, T = 100)

# Modify the starting values by:
sv_list = sv$get_starting_values()   # getting them as list
sv_list$A <- matrix(rnorm(12), 3, 4) # modifying the entry
sv$set_starting_values(sv_list)      # providing to the class object

R6 Class Representing StartingValuesBSVARSV

Description

The class StartingValuesBSVARSV presents starting values for the bsvar model with Stochastic Volatility heteroskedasticity.

Super class

bsvars::StartingValuesBSVAR -> StartingValuesBSVARSV

Public fields

A: an NxK matrix of starting values for the parameter A.
B: an NxN matrix of starting values for the parameter B.
hyper: a (2*N+1)x2 matrix of starting values for the shrinkage hyper-parameters of the hierarchical prior distribution.
h: an NxT matrix with the starting values of the log-volatility processes.
rho: an N-vector with values of SV autoregressive parameters.
omega: an N-vector with values of SV process conditional standard deviations.
sigma2v: an N-vector with values of SV process conditional variances.
S: an NxT integer matrix with the auxiliary mixture component indicators.
sigma2_omega: an N-vector with variances of the zero-mean normal prior for \omega_n.
s_: a positive scalar with the scale of the gamma prior of the hierarchical prior for \sigma^2_{\omega}.

Methods

Public methods

specify_starting_values_bsvar_sv$new()
specify_starting_values_bsvar_sv$get_starting_values()
specify_starting_values_bsvar_sv$set_starting_values()
specify_starting_values_bsvar_sv$clone()

Method `new()`

Create new starting values StartingValuesBSVARSV.

Usage

specify_starting_values_bsvar_sv$new(N, p, T, d = 0)

Arguments

N: a positive integer - the number of dependent variables in the model.
p: a positive integer - the autoregressive lag order of the SVAR model.
T: a positive integer - the the time series dimension of the dependent variable matrix Y.
d: a positive integer - the number of exogenous variables in the model.

Returns

Starting values StartingValuesBSVARSV.

Method `get_starting_values()`

Returns the elements of the starting values StartingValuesBSVARSV as a list.

Usage

specify_starting_values_bsvar_sv$get_starting_values()

Examples

# starting values for a bsvar model with 1 lag for a 3-variable system
sv = specify_starting_values_bsvar_sv$new(N = 3, p = 1, T = 100)
sv$get_starting_values()   # show starting values as list

Method `set_starting_values()`

Returns the elements of the starting values StartingValuesBSVAR_SV as a list.

Usage

specify_starting_values_bsvar_sv$set_starting_values(last_draw)

Arguments

last_draw: a list containing the last draw of the current MCMC run.

Returns

An object of class StartingValuesBSVAR including the last draw of the current MCMC as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Examples

# starting values for a bsvar model with 1 lag for a 3-variable system
sv = specify_starting_values_bsvar_sv$new(N = 3, p = 1, T = 100)

# Modify the starting values by:
sv_list = sv$get_starting_values()   # getting them as list
sv_list$A <- matrix(rnorm(12), 3, 4) # modifying the entry
sv$set_starting_values(sv_list)      # providing to the class object

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_starting_values_bsvar_sv$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

# starting values for a bsvar model for a 3-variable system
sv = specify_starting_values_bsvar_sv$new(N = 3, p = 1, T = 100)


## ------------------------------------------------
## Method `specify_starting_values_bsvar_sv$get_starting_values`
## ------------------------------------------------

# starting values for a bsvar model with 1 lag for a 3-variable system
sv = specify_starting_values_bsvar_sv$new(N = 3, p = 1, T = 100)
sv$get_starting_values()   # show starting values as list


## ------------------------------------------------
## Method `specify_starting_values_bsvar_sv$set_starting_values`
## ------------------------------------------------

# starting values for a bsvar model with 1 lag for a 3-variable system
sv = specify_starting_values_bsvar_sv$new(N = 3, p = 1, T = 100)

# Modify the starting values by:
sv_list = sv$get_starting_values()   # getting them as list
sv_list$A <- matrix(rnorm(12), 3, 4) # modifying the entry
sv$set_starting_values(sv_list)      # providing to the class object

R6 Class Representing StartingValuesBSVART

Description

The class StartingValuesBSVART presents starting values for the bsvar model with t-distributed structural shocks.

Super class

bsvars::StartingValuesBSVAR -> StartingValuesBSVART

Public fields

A: an NxK matrix of starting values for the parameter A.
B: an NxN matrix of starting values for the parameter B.
hyper: a (2*N+1)x2 matrix of starting values for the shrinkage hyper-parameters of the hierarchical prior distribution.
lambda: a Tx1 vector of starting values for latent variables.
df: a positive scalar with starting values for the degrees of freedom parameter of the Student-t conditional distribution of structural shock.

Methods

Public methods

specify_starting_values_bsvar_t$new()
specify_starting_values_bsvar_t$get_starting_values()
specify_starting_values_bsvar_t$set_starting_values()
specify_starting_values_bsvar_t$clone()

Method `new()`

Create new starting values StartingValuesBSVART

Usage

specify_starting_values_bsvar_t$new(N, p, T, d = 0)

Arguments

N: a positive integer - the number of dependent variables in the model.
p: a positive integer - the autoregressive lag order of the SVAR model.
T: a positive integer - the the time series dimension of the dependent variable matrix Y.
d: a positive integer - the number of exogenous variables in the model.

Returns

Starting values StartingValuesBSVART

Method `get_starting_values()`

Returns the elements of the starting values StartingValuesBSVAR as a list.

Usage

specify_starting_values_bsvar_t$get_starting_values()

Examples

# starting values for a homoskedastic bsvar with 1 lag for a 3-variable system
sv = specify_starting_values_bsvar$new(N = 3, p = 1)
sv$get_starting_values()   # show starting values as list

Method `set_starting_values()`

Returns the elements of the starting values StartingValuesBSVAR as a list.

Usage

specify_starting_values_bsvar_t$set_starting_values(last_draw)

Arguments

last_draw: a list containing the last draw of elements B - an NxN matrix, A - an NxK matrix, and hyper - a vector of 5 positive real numbers.

Returns

An object of class StartingValuesBSVAR including the last draw of the current MCMC as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Examples

# starting values for a homoskedastic bsvar with 1 lag for a 3-variable system
sv = specify_starting_values_bsvar$new(N = 3, p = 1)

# Modify the starting values by:
sv_list = sv$get_starting_values()   # getting them as list
sv_list$A <- matrix(rnorm(12), 3, 4) # modifying the entry
sv$set_starting_values(sv_list)      # providing to the class object

Method `clone()`

The objects of this class are cloneable with this method.

Usage

specify_starting_values_bsvar_t$clone(deep = FALSE)

Arguments

deep: Whether to make a deep clone.

Examples

# starting values for a bsvar model for a 3-variable system
sv = specify_starting_values_bsvar_t$new(N = 3, p = 1, T = 100)


## ------------------------------------------------
## Method `specify_starting_values_bsvar_t$get_starting_values`
## ------------------------------------------------

# starting values for a homoskedastic bsvar with 1 lag for a 3-variable system
sv = specify_starting_values_bsvar$new(N = 3, p = 1)
sv$get_starting_values()   # show starting values as list


## ------------------------------------------------
## Method `specify_starting_values_bsvar_t$set_starting_values`
## ------------------------------------------------

# starting values for a homoskedastic bsvar with 1 lag for a 3-variable system
sv = specify_starting_values_bsvar$new(N = 3, p = 1)

# Modify the starting values by:
sv_list = sv$get_starting_values()   # getting them as list
sv_list$A <- matrix(rnorm(12), 3, 4) # modifying the entry
sv$set_starting_values(sv_list)      # providing to the class object

Provides posterior summary of Forecasts

Description

Provides posterior summary of the forecasts including their mean, standard deviations, as well as 5 and 95 percentiles.

Usage

## S3 method for class 'Forecasts'
summary(object, ...)

Arguments

object

an object of class Forecasts obtained using the forecast() function containing draws the predictive density.

...

additional arguments affecting the summary produced.

Value

A list reporting the posterior mean, standard deviations, as well as 5 and 95 percentiles of the forecasts for each of the variables and forecast horizons.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# forecast
fore           = forecast(posterior, horizon = 2)
fore_summary   = summary(fore)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  forecast(horizon = 2) |>
  summary() -> fore_summary

Provides posterior summary of homoskedastic Structural VAR estimation

Description

Provides posterior mean, standard deviations, as well as 5 and 95 percentiles of the parameters: the structural matrix B, autoregressive parameters A, and hyper parameters.

Usage

## S3 method for class 'PosteriorBSVAR'
summary(object, ...)

Arguments

object

an object of class PosteriorBSVAR obtained using the estimate() function applied to homoskedastic Bayesian Structural VAR model specification set by function specify_bsvar$new() containing draws from the posterior distribution of the parameters.

...

additional arguments affecting the summary produced.

Value

A list reporting the posterior mean, standard deviations, as well as 5 and 95 percentiles of the parameters: the structural matrix B, autoregressive parameters A, and hyper-parameters.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)
summary(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  summary()

Provides posterior summary of non-normal Structural VAR estimation

Description

Provides posterior mean, standard deviations, as well as 5 and 95 percentiles of the parameters: the structural matrix B, autoregressive parameters A, and hyper parameters.

Usage

## S3 method for class 'PosteriorBSVARMIX'
summary(object, ...)

Arguments

object

an object of class PosteriorBSVARMIX obtained using the estimate() function applied to non-normal Bayesian Structural VAR model specification set by function specify_bsvar_mix$new() containing draws from the posterior distribution of the parameters.

...

additional arguments affecting the summary produced.

Value

A list reporting the posterior mean, standard deviations, as well as 5 and 95 percentiles of the parameters: the structural matrix B, autoregressive parameters A, and hyper-parameters.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_mix$new(us_fiscal_lsuw)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)
summary(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_mix$new() |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  summary()

Provides posterior summary of heteroskedastic Structural VAR estimation

Description

Provides posterior mean, standard deviations, as well as 5 and 95 percentiles of the parameters: the structural matrix B, autoregressive parameters A, and hyper parameters.

Usage

## S3 method for class 'PosteriorBSVARMSH'
summary(object, ...)

Arguments

object

an object of class PosteriorBSVARMSH obtained using the estimate() function applied to heteroskedastic Bayesian Structural VAR model specification set by function specify_bsvar_msh$new() containing draws from the posterior distribution of the parameters.

...

additional arguments affecting the summary produced.

Value

A list reporting the posterior mean, standard deviations, as well as 5 and 95 percentiles of the parameters: the structural matrix B, autoregressive parameters A, and hyper-parameters.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_msh$new(us_fiscal_lsuw)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)
summary(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new() |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  summary()

Provides posterior summary of heteroskedastic Structural VAR estimation

Description

Provides posterior mean, standard deviations, as well as 5 and 95 percentiles of the parameters: the structural matrix B, autoregressive parameters A, and hyper parameters.

Usage

## S3 method for class 'PosteriorBSVARSV'
summary(object, ...)

Arguments

object

an object of class PosteriorBSVARSV obtained using the estimate() function applied to heteroskedastic Bayesian Structural VAR model specification set by function specify_bsvar_sv$new() containing draws from the posterior distribution of the parameters.

...

additional arguments affecting the summary produced.

Value

A list reporting the posterior mean, standard deviations, as well as 5 and 95 percentiles of the parameters: the structural matrix B, autoregressive parameters A, and hyper-parameters.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_sv$new(us_fiscal_lsuw)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)
summary(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new() |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  summary()

Provides posterior summary of Structural VAR with t-distributed shocks estimation

Description

Provides posterior mean, standard deviations, as well as 5 and 95 percentiles of the parameters: the structural matrix B, autoregressive parameters A, hyper-parameters, and Student-t degrees-of-freedom parameter \nu.

Usage

## S3 method for class 'PosteriorBSVART'
summary(object, ...)

Arguments

object

an object of class PosteriorBSVART obtained using the estimate() function applied to homoskedastic Bayesian Structural VAR model specification set by function specify_bsvar$new() containing draws from the posterior distribution of the parameters.

...

additional arguments affecting the summary produced.

Value

A list reporting the posterior mean, standard deviations, as well as 5 and 95 percentiles of the parameters: the structural matrix B, autoregressive parameters A, hyper-parameters, and Student-t degrees-of-freedom parameter \nu.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_t$new(us_fiscal_lsuw)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)
summary(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_t$new() |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  summary()

Provides posterior summary of forecast error variance decompositions

Description

Provides posterior means of the forecast error variance decompositions of each variable at all horizons.

Usage

## S3 method for class 'PosteriorFEVD'
summary(object, ...)

Arguments

object

an object of class PosteriorFEVD obtained using the compute_variance_decompositions() function containing draws from the posterior distribution of the forecast error variance decompositions.

...

additional arguments affecting the summary produced.

Value

A list reporting the posterior mean of the forecast error variance decompositions of each variable at all horizons.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute forecast error variance decompositions
fevd           = compute_variance_decompositions(posterior, horizon = 4)
fevd_summary   = summary(fevd)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_variance_decompositions(horizon = 4) |>
  summary() -> fevd_summary

Provides posterior summary of variables' fitted values

Description

Provides posterior summary of the fitted values including their mean, standard deviations, as well as 5 and 95 percentiles.

Usage

## S3 method for class 'PosteriorFitted'
summary(object, ...)

Arguments

object

an object of class PosteriorFitted obtained using the compute_fitted_values() function containing draws the predictive density of the sample data.

...

additional arguments affecting the summary produced.

Value

A list reporting the posterior mean, standard deviations, as well as 5 and 95 percentiles of the fitted values for each of the shocks and periods.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute fitted values
fitted         = compute_fitted_values(posterior)
fitted_summary = summary(fitted)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_fitted_values() |>
  summary() -> fitted_summary

Provides posterior summary of historical decompositions

Description

Provides posterior means of the historical decompositions variable by variable.

Usage

## S3 method for class 'PosteriorHD'
summary(object, ...)

Arguments

object

an object of class PosteriorHD obtained using the compute_historical_decompositions() function containing posterior draws of historical decompositions.

...

additional arguments affecting the summary produced.

Value

A list reporting the posterior means of historical decompositions for each of the variables.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(diff(us_fiscal_lsuw))

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute historical decompositions
hds            = compute_historical_decompositions(posterior)
hds_summary    = summary(hds)

# workflow with the pipe |>
############################################################
set.seed(123)
diff(us_fiscal_lsuw) |>
  specify_bsvar$new() |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_historical_decompositions() |>
  summary() -> hds_summary

Provides posterior summary of impulse responses

Description

Provides posterior summary of the impulse responses of each variable to each of the shocks at all horizons. Includes their posterior means, standard deviations, as well as 5 and 95 percentiles.

Usage

## S3 method for class 'PosteriorIR'
summary(object, ...)

Arguments

object

an object of class PosteriorIR obtained using the compute_impulse_responses() function containing draws from the posterior distribution of the impulse responses.

...

additional arguments affecting the summary produced.

Value

A list reporting the posterior mean, standard deviations, as well as 5 and 95 percentiles of the impulse responses of each variable to each of the shocks at all horizons.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute impulse responses
irf            = compute_impulse_responses(posterior, horizon = 4)
irf_summary    = summary(irf)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_impulse_responses(horizon = 4) |>
  summary() -> irf_summary

Provides posterior summary of regime probabilities

Description

Provides posterior summary of regime probabilities including their mean, standard deviations, as well as 5 and 95 percentiles.

Usage

## S3 method for class 'PosteriorRegimePr'
summary(object, ...)

Arguments

object

an object of class PosteriorRegimePr obtained using the compute_regime_probabilities() function containing posterior draws of regime allocations.

...

additional arguments affecting the summary produced.

Value

A list reporting the posterior mean and standard deviations of the regime probabilities.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_msh$new(us_fiscal_lsuw)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute regime probabilities
rp             = compute_regime_probabilities(posterior)
rp_summary     = summary(rp)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new() |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_regime_probabilities() |>
  summary() -> rp_summary

Provides posterior summary of structural shocks

Description

Provides posterior summary of the structural shocks including their mean, standard deviations, as well as 5 and 95 percentiles.

Usage

## S3 method for class 'PosteriorShocks'
summary(object, ...)

Arguments

object

an object of class PosteriorShocks obtained using the compute_structural_shocks() function containing draws the posterior distribution of the structural shocks.

...

additional arguments affecting the summary produced.

Value

A list reporting the posterior mean, standard deviations, as well as 5 and 95 percentiles of the structural shocks for each of the equations and periods.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar$new(us_fiscal_lsuw)

# run the burn-in
burn_in        = estimate(specification, 10)

# estimate the model
posterior      = estimate(burn_in, 20)

# compute structural shocks
shocks         = compute_structural_shocks(posterior)
shocks_summary = summary(shocks)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 10) |> 
  estimate(S = 20) |> 
  compute_structural_shocks() |>
  summary() -> shocks_summary

Provides posterior summary of structural shocks' conditional standard deviations

Description

Provides posterior summary of structural shocks' conditional standard deviations including their mean, standard deviations, as well as 5 and 95 percentiles.

Usage

## S3 method for class 'PosteriorSigma'
summary(object, ...)

Arguments

object

an object of class PosteriorSigma obtained using the compute_conditional_sd() function containing posterior draws of conditional standard deviations of structural shocks.

...

additional arguments affecting the summary produced.

Value

A list reporting the posterior mean, standard deviations, as well as 5 and 95 percentiles of the structural shocks' conditional standard deviations for each of the shocks and periods.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
set.seed(123)
specification  = specify_bsvar_sv$new(us_fiscal_lsuw)

# run the burn-in
burn_in        = estimate(specification, 5)

# estimate the model
posterior      = estimate(burn_in, 5)

# compute structural shocks' conditional standard deviations
sigma          = compute_conditional_sd(posterior)
sigma_summary  = summary(sigma)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  compute_conditional_sd() |>
  summary() -> sigma_summary

Provides summary of verifying hypotheses about autoregressive parameters

Description

Provides summary of the Savage-Dickey density ratios for verification of hypotheses about autoregressive parameters.

Usage

## S3 method for class 'SDDRautoregression'
summary(object, ...)

Arguments

object

an object of class SDDRautoregression obtained using the verify_autoregression() function.

...

additional arguments affecting the summary produced.

Value

A table reporting the logarithm of Bayes factors of the restriction against no restriction posterior odds in "log(SDDR)", its numerical standard error "NSE", and the implied posterior probability of the restriction holding or not hypothesis, "Pr[H0|data]" and "Pr[H1|data]" respectively.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify autoregression
H0             = matrix(NA, ncol(us_fiscal_lsuw), ncol(us_fiscal_lsuw) + 1)
H0[1,3]        = 0        # a hypothesis of no Granger causality from gdp to ttr
sddr           = verify_autoregression(posterior, H0)
summary(sddr)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1) |>
  estimate(S = 10) |> 
  verify_autoregression(hypothesis = H0) |> 
  summary() -> sddr_summary

Provides summary of verifying shocks' normality

Description

Provides summary of the Savage-Dickey density ratios for verification of structural shocks normality. The outcomes can be used to make probabilistic statements about identification through non-normality.

Usage

## S3 method for class 'SDDRidMIX'
summary(object, ...)

Arguments

object

an object of class SDDRidMIX obtained using the verify_identification.PosteriorBSVARMIX function.

...

additional arguments affecting the summary produced.

Value

A table reporting the logarithm of Bayes factors of normal to non-normal shocks posterior odds "log(SDDR)" for each structural shock, their numerical standard errors "NSE", and the implied posterior probability of the normality and non-normality hypothesis, "Pr[normal|data]" and "Pr[non-normal|data]" respectively.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, M = 2)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify heteroskedasticity
sddr           = verify_identification(posterior)
summary(sddr)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_mix$new(M = 2) |>
  estimate(S = 10) |> 
  verify_identification() |> 
  summary() -> sddr_summary

Provides summary of verifying homoskedasticity

Description

Provides summary of the Savage-Dickey density ratios for verification of structural shocks homoskedasticity. The outcomes can be used to make probabilistic statements about identification through heteroskedasticity closely following ideas by Lütkepohl& Woźniak (2020).

Usage

## S3 method for class 'SDDRidMSH'
summary(object, ...)

Arguments

object

an object of class SDDRidMSH obtained using the verify_identification.PosteriorBSVARMSH function.

...

additional arguments affecting the summary produced.

Value

A table reporting the logarithm of Bayes factors of homoskedastic to heteroskedastic posterior odds "log(SDDR)" for each structural shock, their numerical standard errors "NSE", and the implied posterior probability of the homoskedasticity and heteroskedasticity hypothesis, "Pr[homoskedasticity|data]" and "Pr[heteroskedasticity|data]" respectively.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, M = 2)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify heteroskedasticity
sddr           = verify_identification(posterior)
summary(sddr)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new(M = 2) |>
  estimate(S = 10) |> 
  verify_identification() |> 
  summary() -> sddr_summary

Provides summary of verifying homoskedasticity

Description

Provides summary of the Savage-Dickey density ratios for verification of structural shocks homoskedasticity. The outcomes can be used to make probabilistic statements about identification through heteroskedasticity following Lütkepohl, Shang, Uzeda & Woźniak (2024).

Usage

## S3 method for class 'SDDRidSV'
summary(object, ...)

Arguments

object

an object of class SDDRidSV obtained using the verify_identification.PosteriorBSVARSV function.

...

additional arguments affecting the summary produced.

Value

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_sv$new(us_fiscal_lsuw)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify heteroskedasticity
sddr           = verify_identification(posterior)
summary(sddr)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new() |>
  estimate(S = 10) |> 
  verify_identification() |> 
  summary() -> sddr_summary

Provides summary of verifying shocks' normality

Description

Usage

## S3 method for class 'SDDRidT'
summary(object, ...)

Arguments

object

an object of class SDDRidT obtained using the verify_identification.PosteriorBSVART function.

...

additional arguments affecting the summary produced.

Value

A table reporting the Bayes factor of normal to Student-t shocks posterior odds "SDDR" as well as its logarithm "log(SDDR)"for each structural shock, and the implied posterior probability of the normality and Student-t hypothesis, "Pr[normal|data]" and "Pr[Student-t|data]" respectively.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_t$new(us_fiscal_lsuw)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify heteroskedasticity
sddr           = verify_identification(posterior)
summary(sddr)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_t$new() |>
  estimate(S = 10) |> 
  verify_identification() |> 
  summary() -> sddr_summary

Provides summary of verifying homoskedasticity

Description

Provides summary of the Savage-Dickey density ratios for verification of structural shocks homoskedasticity.

Usage

## S3 method for class 'SDDRvolatility'
summary(object, ...)

Arguments

object

an object of class SDDRvolatility obtained using the verify_volatility() function.

...

additional arguments affecting the summary produced.

Value

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 1, M = 2)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify heteroskedasticity
sddr           = verify_volatility(posterior)
summary(sddr)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  verify_volatility() |> 
  summary() -> sddr_summary

A matrix to be used in a conditional forecasting example including the projected values of total tax revenue that are projected to increase at an average quarterly sample growth rate. The other two columns are filled with `NA` values, which implies that the future values of the corresponding endogenous variables, namely government spending and GDP, will be forecasted given the provided projected values of total tax revenue. The matrix includes future values for the forecast horizon of two years for the US fiscal model for the period 2024 Q3 – 2026 Q2.

Description

Conditional projections variables to be used in conditional forecasting of government spending and GDP given the provided projected values of total tax revenue. Last data update was implemented on 2024-10-22.

Usage

data(us_fiscal_cond_forecasts)

Format

A matrix and a ts object with time series of eight values on 3 variables:

ttr: the values are provided. This variable will not be forecasted.
gs: not provided. This variable will be forecasted conditionally on the provided values for ttr.
gdp: not provided. This variable will be forecasted conditionally on the provided values for ttr

The series are as described by Mertens & Ravn (2014). The data was used by Lütkepohl, Shang, Uzeda, Woźniak (2024).

References

Mertens, K., and Ravn, M.O. (2014) A Reconciliation of SVAR and Narrative Estimates of Tax Multipliers, Journal of Monetary Economics, 68(S), S1–S19. DOI: doi:10.1016/j.jmoneco.2013.04.004.

Examples

data(us_fiscal_cond_forecasts)   # upload the data

A 3-variable system of exogenous variables for the US fiscal model for the period 1948 Q1 – 2024 Q2

Description

Exogenous variables used to identify the US fiscal policy shocks. Last data update was implemented on 2024-10-20.

Usage

data(us_fiscal_ex)

Format

A matrix and a ts object with time series of over three hundred observations on 3 variables:

t: a time trend
t^2: a quadratic trend
1975Q2: a dummy variable taking the value of 1 for quarter 2 1975 and zero elsewhere

The series are as described by Mertens & Ravn (2014). The data was used by Lütkepohl, Shang, Uzeda, Woźniak (2024).

References

Mertens, K., and Ravn, M.O. (2014) A Reconciliation of SVAR and Narrative Estimates of Tax Multipliers, Journal of Monetary Economics, 68(S), S1–S19. DOI: doi:10.1016/j.jmoneco.2013.04.004.

Examples

data(us_fiscal_ex)   # upload the data
plot(us_fiscal_ex)   # plot the data

A 3-variable system of exogenous variables' future values for the forecast horizon of two years for the US fiscal model for the period 2024 Q3 – 2026 Q2

Description

Exogenous variables to be used in forecasting of the US fiscal policy shocks. Last data update was implemented on 2024-10-22.

Usage

data(us_fiscal_ex_forecasts)

Format

A matrix and a ts object with time series of eight values on 3 variables:

t: a time trend
t^2: a quadratic trend
1975Q2: a dummy variable taking the value of 1 for quarter 2 1975 and zero elsewhere

The series are as described by Mertens & Ravn (2014). The data was used by Lütkepohl, Shang, Uzeda, Woźniak (2024).

References

Mertens, K., and Ravn, M.O. (2014) A Reconciliation of SVAR and Narrative Estimates of Tax Multipliers, Journal of Monetary Economics, 68(S), S1–S19. DOI: doi:10.1016/j.jmoneco.2013.04.004.

Examples

data(us_fiscal_ex_forecasts)   # upload the data

A 3-variable US fiscal system for the period 1948 Q1 – 2024 Q2

Description

A system used to identify the US fiscal policy shocks. Last data update was implemented on 2024-10-20.

Usage

data(us_fiscal_lsuw)

Format

A matrix and a ts object with time series of over three hundred observations on 3 variables:

ttr: quarterly US total tax revenue expressed in log, real, per person terms
gs: quarterly US total government spending expressed in log, real, per person terms
gdp: quarterly US gross domestic product expressed in log, real, per person terms

The series are as described by Mertens & Ravn (2014) in footnote 3 and main body on page S3 of the paper. Differences with respect to Mertens & Ravn's data :

The sample period is from quarter 1 of 1948 to the last available observation,
The population variable is not from Francis & Ramey (2009) but from the FRED (with the same definition),
The original monthly population data is transformed to quarterly by taking monthly averages.

Source

U.S. Bureau of Economic Analysis, National Income and Product Accounts, https://www.bea.gov/

FRED Economic Database, Federal Reserve Bank of St. Louis, https://fred.stlouisfed.org/

References

Francis, N., and Ramey, V.A. (2009) Measures of per capita Hours and Their Implications for the Technology‐hours Debate. Journal of Money, Credit and Banking, 41(6), 1071-1097, DOI: doi:10.1111/j.1538-4616.2009.00247.x.

Mertens, K., and Ravn, M.O. (2014) A Reconciliation of SVAR and Narrative Estimates of Tax Multipliers, Journal of Monetary Economics, 68(S), S1–S19. DOI: doi:10.1016/j.jmoneco.2013.04.004.

Examples

data(us_fiscal_lsuw)   # upload the data
plot(us_fiscal_lsuw)   # plot the data

Verifies hypotheses involving autoregressive parameters

Description

Computes the logarithm of Bayes factor for the joint hypothesis, H_0, possibly for many autoregressive parameters represented by argument hypothesis via Savage-Dickey Density Ration (SDDR). The logarithm of Bayes factor for this hypothesis can be computed using the SDDR as the difference of logarithms of the marginal posterior distribution ordinate at the restriction less the marginal prior distribution ordinate at the same point:

log p(H_0 | data) - log p(H_0)

Therefore, a negative value of the difference is the evidence against hypothesis. The estimation of both elements of the difference requires numerical integration.

Usage

verify_autoregression(posterior, hypothesis)

Arguments

posterior

the posterior element of the list from the estimation outcome

hypothesis

an NxK matrix of the same dimension as the autoregressive matrix A with numeric values for the parameters to be verified, in which case the values represent the joint hypothesis, and missing value NA for these parameters that are not tested

Value

An object of class SDDRautoregression that is a list of three components:

logSDDR a scalar with values of the logarithm of the Bayes factors for the autoregressive hypothesis for each of the shocks

log_SDDR_se an N-vector with estimation standard errors of the logarithm of the Bayes factors reported in output element logSDDR that are computed based on 30 random sub-samples of the log-ordinates of the marginal posterior and prior distributions.

components a list of three components for the computation of the Bayes factor

log_denominator: an N-vector with values of the logarithm of the Bayes factor denominators
log_numerator: an N-vector with values of the logarithm of the Bayes factor numerators
log_numerator_s: an NxS matrix of the log-full conditional posterior density ordinates computed to estimate the numerator
log_denominator_s: an NxS matrix of the log-full conditional posterior density ordinates computed to estimate the denominator
se_components: a 30-vector containing the log-Bayes factors on the basis of which the standard errors are computed

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Woźniak, T., and Droumaguet, M., (2024) Bayesian Assessment of Identifying Restrictions for Heteroskedastic Structural VARs

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify autoregression
H0             = matrix(NA, ncol(us_fiscal_lsuw), ncol(us_fiscal_lsuw) + 1)
H0[1,3]        = 0        # a hypothesis of no Granger causality from gdp to ttr
sddr           = verify_autoregression(posterior, H0)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 10) |> 
  verify_autoregression(hypothesis = H0) -> sddr

Verifies hypotheses involving autoregressive parameters

Description

log p(H_0 | data) - log p(H_0)

Therefore, a negative value of the difference is the evidence against hypothesis. The estimation of both elements of the difference requires numerical integration.

Usage

## S3 method for class 'PosteriorBSVAR'
verify_autoregression(posterior, hypothesis)

Arguments

posterior

the posterior element of the list from the estimation outcome

hypothesis

Value

An object of class SDDRautoregression that is a list of three components:

logSDDR a scalar with values of the logarithm of the Bayes factors for the autoregressive hypothesis for each of the shocks

components a list of three components for the computation of the Bayes factor

log_denominator: an N-vector with values of the logarithm of the Bayes factor denominators
log_numerator: an N-vector with values of the logarithm of the Bayes factor numerators
log_numerator_s: an NxS matrix of the log-full conditional posterior density ordinates computed to estimate the numerator
log_denominator_s: an NxS matrix of the log-full conditional posterior density ordinates computed to estimate the denominator
se_components: a 30-vector containing the log-Bayes factors on the basis of which the standard errors are computed

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Woźniak, T., and Droumaguet, M., (2024) Bayesian Assessment of Identifying Restrictions for Heteroskedastic Structural VARs

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify autoregression
H0             = matrix(NA, ncol(us_fiscal_lsuw), ncol(us_fiscal_lsuw) + 1)
H0[1,3]        = 0        # a hypothesis of no Granger causality from gdp to ttr
sddr           = verify_autoregression(posterior, H0)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 10) |> 
  verify_autoregression(hypothesis = H0) -> sddr

Verifies hypotheses involving autoregressive parameters

Description

log p(H_0 | data) - log p(H_0)

Therefore, a negative value of the difference is the evidence against hypothesis. The estimation of both elements of the difference requires numerical integration.

Usage

## S3 method for class 'PosteriorBSVARMIX'
verify_autoregression(posterior, hypothesis)

Arguments

posterior

the posterior element of the list from the estimation outcome

hypothesis

Value

An object of class SDDRautoregression that is a list of three components:

logSDDR a scalar with values of the logarithm of the Bayes factors for the autoregressive hypothesis for each of the shocks

components a list of three components for the computation of the Bayes factor

log_denominator: an N-vector with values of the logarithm of the Bayes factor denominators
log_numerator: an N-vector with values of the logarithm of the Bayes factor numerators
log_numerator_s: an NxS matrix of the log-full conditional posterior density ordinates computed to estimate the numerator
log_denominator_s: an NxS matrix of the log-full conditional posterior density ordinates computed to estimate the denominator
se_components: a 30-vector containing the log-Bayes factors on the basis of which the standard errors are computed

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Woźniak, T., and Droumaguet, M., (2024) Bayesian Assessment of Identifying Restrictions for Heteroskedastic Structural VARs

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 1, M = 2)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify autoregression
H0             = matrix(NA, ncol(us_fiscal_lsuw), ncol(us_fiscal_lsuw) + 1)
H0[1,3]        = 0        # a hypothesis of no Granger causality from gdp to ttr
sddr           = verify_autoregression(posterior, H0)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_mix$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  verify_autoregression(hypothesis = H0) -> sddr

Verifies hypotheses involving autoregressive parameters

Description

log p(H_0 | data) - log p(H_0)

Therefore, a negative value of the difference is the evidence against hypothesis. The estimation of both elements of the difference requires numerical integration.

Usage

## S3 method for class 'PosteriorBSVARMSH'
verify_autoregression(posterior, hypothesis)

Arguments

posterior

the posterior element of the list from the estimation outcome

hypothesis

Value

An object of class SDDRautoregression that is a list of three components:

logSDDR a scalar with values of the logarithm of the Bayes factors for the autoregressive hypothesis for each of the shocks

components a list of three components for the computation of the Bayes factor

log_denominator: an N-vector with values of the logarithm of the Bayes factor denominators
log_numerator: an N-vector with values of the logarithm of the Bayes factor numerators
log_numerator_s: an NxS matrix of the log-full conditional posterior density ordinates computed to estimate the numerator
log_denominator_s: an NxS matrix of the log-full conditional posterior density ordinates computed to estimate the denominator
se_components: a 30-vector containing the log-Bayes factors on the basis of which the standard errors are computed

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Woźniak, T., and Droumaguet, M., (2024) Bayesian Assessment of Identifying Restrictions for Heteroskedastic Structural VARs

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 1, M = 2)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify autoregression
H0             = matrix(NA, ncol(us_fiscal_lsuw), ncol(us_fiscal_lsuw) + 1)
H0[1,3]        = 0        # a hypothesis of no Granger causality from gdp to ttr
sddr           = verify_autoregression(posterior, H0)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  verify_autoregression(hypothesis = H0) -> sddr

Verifies hypotheses involving autoregressive parameters

Description

log p(H_0 | data) - log p(H_0)

Therefore, a negative value of the difference is the evidence against hypothesis. The estimation of both elements of the difference requires numerical integration.

Usage

## S3 method for class 'PosteriorBSVARSV'
verify_autoregression(posterior, hypothesis)

Arguments

posterior

the posterior element of the list from the estimation outcome

hypothesis

Value

An object of class SDDRautoregression that is a list of three components:

logSDDR a scalar with values of the logarithm of the Bayes factors for the autoregressive hypothesis for each of the shocks

components a list of three components for the computation of the Bayes factor

log_denominator: an N-vector with values of the logarithm of the Bayes factor denominators
log_numerator: an N-vector with values of the logarithm of the Bayes factor numerators
log_numerator_s: an NxS matrix of the log-full conditional posterior density ordinates computed to estimate the numerator
log_denominator_s: an NxS matrix of the log-full conditional posterior density ordinates computed to estimate the denominator
se_components: a 30-vector containing the log-Bayes factors on the basis of which the standard errors are computed

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Woźniak, T., and Droumaguet, M., (2024) Bayesian Assessment of Identifying Restrictions for Heteroskedastic Structural VARs

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify autoregression
H0             = matrix(NA, ncol(us_fiscal_lsuw), ncol(us_fiscal_lsuw) + 1)
H0[1,3]        = 0        # a hypothesis of no Granger causality from gdp to ttr
sddr           = verify_autoregression(posterior, H0)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1) |>
  estimate(S = 10) |> 
  verify_autoregression(hypothesis = H0) -> sddr

Verifies hypotheses involving autoregressive parameters

Description

log p(H_0 | data) - log p(H_0)

Therefore, a negative value of the difference is the evidence against hypothesis. The estimation of both elements of the difference requires numerical integration.

Usage

## S3 method for class 'PosteriorBSVART'
verify_autoregression(posterior, hypothesis)

Arguments

posterior

the posterior element of the list from the estimation outcome

hypothesis

Value

An object of class SDDRautoregression that is a list of three components:

logSDDR a scalar with values of the logarithm of the Bayes factors for the autoregressive hypothesis for each of the shocks

components a list of three components for the computation of the Bayes factor

log_denominator: an N-vector with values of the logarithm of the Bayes factor denominators
log_numerator: an N-vector with values of the logarithm of the Bayes factor numerators
log_numerator_s: an NxS matrix of the log-full conditional posterior density ordinates computed to estimate the numerator
log_denominator_s: an NxS matrix of the log-full conditional posterior density ordinates computed to estimate the denominator
se_components: a 30-vector containing the log-Bayes factors on the basis of which the standard errors are computed

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Woźniak, T., and Droumaguet, M., (2024) Bayesian Assessment of Identifying Restrictions for Heteroskedastic Structural VARs

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_t$new(us_fiscal_lsuw)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify autoregression
H0             = matrix(NA, ncol(us_fiscal_lsuw), ncol(us_fiscal_lsuw) + 1)
H0[1,3]        = 0        # a hypothesis of no Granger causality from gdp to ttr
sddr           = verify_autoregression(posterior, H0)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_t$new() |>
  estimate(S = 10) |> 
  verify_autoregression(hypothesis = H0) -> sddr

Verifies identification through heteroskedasticity or non-normality of of structural shocks

Description

Computes the logarithm of Bayes factor(s) for the hypothesis in which the model is not identified through heteroskedasticity of non-normality using Savage-Dickey Density Ration (SDDR). The hypothesis of no such identification, H_0, is represented by model-specific restrictions.Consult help files for individual classes of models for details. The logarithm of Bayes factor for this hypothesis can be computed using the SDDR as the difference of the logarithm of the marginal posterior distribution ordinate at the restriction less the log-marginal prior distribution ordinate at the same point:

log p(H_0 | data) - log p(H_0)

Therefore, a negative value of the difference is the evidence against the lack of identification of the structural shock through heteroskedasticity or non-normality.

Usage

verify_identification(posterior)

Arguments

posterior

the estimation outcome obtained using estimate function

Value

An object of class SDDRid* that is a list with components:

logSDDR a vector with values of the logarithm of the Bayes factors

log_SDDR_se a vector with numerical standard errors of the logarithm of the Bayes factors reported in output element logSDDR that are computed based on 30 random sub-samples of the log-ordinates of the marginal posterior and prior distributions.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify heteroskedasticity
sddr           = verify_identification(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1) |>
  estimate(S = 10) |> 
  verify_identification() -> sddr

Verifies identification through heteroskedasticity or non-normality of of structural shocks

Description

Displays information that the model is homoskedastic and with normal shocks.

Usage

## S3 method for class 'PosteriorBSVAR'
verify_identification(posterior)

Arguments

posterior

the estimation outcome obtained using estimate function

Value

Nothing. Just displays a message.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify heteroskedasticity
sddr           = verify_identification(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 10) |> 
  verify_identification() -> sddr

Verifies identification through heteroskedasticity or non-normality of of structural shocks

Description

Computes the logarithm of Bayes factor for the hypothesis of normality for each of the structural shocks via Savage-Dickey Density Ration (SDDR). The hypothesis of normality in this mixture of normals model is represented by restriction:

H_0: \sigma^2_{n.1} = ... = \sigma^2_{n.M} = 1

The logarithm of Bayes factor for this hypothesis can be computed using the SDDR as the difference of logarithms of the marginal posterior distribution ordinate at the restriction less the marginal prior distribution ordinate at the same point:

log p(H_0 | data) - log p(H_0)

Therefore, a negative value of the difference is the evidence against homoskedasticity of the structural shock. The estimation of both elements of the difference requires numerical integration.

Usage

## S3 method for class 'PosteriorBSVARMIX'
verify_identification(posterior)

Arguments

posterior

the estimation outcome obtained using estimate function

Value

An object of class SDDRid* that is a list with components:

logSDDR a vector with values of the logarithm of the Bayes factors

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 1, M = 2)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify heteroskedasticity
sddr           = verify_identification(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_mix$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  verify_identification() -> sddr

Verifies identification through heteroskedasticity or non-normality of of structural shocks

Description

H_0: \sigma^2_{n.1} = ... = \sigma^2_{n.M} = 1

log p(H_0 | data) - log p(H_0)

Therefore, a negative value of the difference is the evidence against homoskedasticity of the structural shock. The estimation of both elements of the difference requires numerical integration.

Usage

## S3 method for class 'PosteriorBSVARMSH'
verify_identification(posterior)

Arguments

posterior

the estimation outcome obtained using estimate function

Value

An object of class SDDRid* that is a list with components:

logSDDR a vector with values of the logarithm of the Bayes factors

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 1, M = 2)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify heteroskedasticity
sddr           = verify_identification(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  verify_identification() -> sddr

Verifies identification through heteroskedasticity or non-normality of of structural shocks

Description

Computes the logarithm of Bayes factor for the homoskedasticity hypothesis for each of the structural shocks via Savage-Dickey Density Ratio (SDDR). The hypothesis of homoskedasticity for the structural shock n is represented by restriction:

H_0: \omega_n = 0

The logarithm of Bayes factor for this hypothesis can be computed using the SDDR as the difference of the logarithm of the marginal posterior distribution ordinate at the restriction less the log-marginal prior distribution ordinate at the same point:

log p(\omega_n = 0 | data) - log p(\omega_n = 0)

Therefore, a negative value of the difference is the evidence against homoskedasticity of the structural shock. The estimation of both elements of the difference requires numerical integration.

Usage

## S3 method for class 'PosteriorBSVARSV'
verify_identification(posterior)

Arguments

posterior

the estimation outcome obtained using estimate function

Value

An object of class SDDRid* that is a list with components:

logSDDR a vector with values of the logarithm of the Bayes factors

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify heteroskedasticity
sddr           = verify_identification(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1) |>
  estimate(S = 10) |> 
  verify_identification() -> sddr

Verifies identification through heteroskedasticity or non-normality of of structural shocks

Description

Computes the logarithm of Bayes factor for the hypothesis of normality of the joint conditional distribution of the structural shocks via Savage-Dickey Density Ration (SDDR). The hypothesis of normality in this t-distributed shocks model is represented by restriction setting the degrees-of-freedom parameter \nu to infinity:

H_0: \nu = \infty

log p(H_0 | data) - log p(H_0)

Therefore, a negative value of the difference is the evidence against homoskedasticity of the structural shock. The estimation of the marginal posterior ordinate is done using truncated Gaussian kernel smoothing.

Usage

## S3 method for class 'PosteriorBSVART'
verify_identification(posterior)

Arguments

posterior

the estimation outcome obtained using estimate function

Value

An object of class SDDRidT that is a list with components:

logSDDR the value of the logarithm of the Bayes factor

SDDR the value of the Bayes factor

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_t$new(us_fiscal_lsuw)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify heteroskedasticity
sddr           = verify_identification(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_t$new() |>
  estimate(S = 10) |> 
  verify_identification() -> sddr

Verifies heteroskedasticity of structural shocks equation by equation

Description

This function will be deprecated starting from version 4.0. It is replaced by verify_identification function.

Computes the logarithm of Bayes factor for the homoskedasticity hypothesis for each of the structural shocks via Savage-Dickey Density Ration (SDDR). The hypothesis of homoskedasticity, H_0, is represented by model-specific restrictions. Consult help files for individual classes of models for details. The logarithm of Bayes factor for this hypothesis can be computed using the SDDR as the difference of logarithms of the marginal posterior distribution ordinate at the restriction less the marginal prior distribution ordinate at the same point:

log p(H_0 | data) - log p(H_0)

Therefore, a negative value of the difference is the evidence against homoskedasticity of the structural shock. The estimation of both elements of the difference requires numerical integration.

Usage

verify_volatility(posterior)

Arguments

posterior

the posterior element of the list from the estimation outcome

Value

An object of class SDDRvolatility that is a list of three components:

logSDDR an N-vector with values of the logarithm of the Bayes factors for the homoskedasticity hypothesis for each of the shocks

components a list of three components for the computation of the Bayes factor

log_denominator: an N-vector with values of the logarithm of the Bayes factor denominators
log_numerator: an N-vector with values of the logarithm of the Bayes factor numerators
log_numerator_s: an NxS matrix of the log-full conditional posterior density ordinates computed to estimate the numerator
se_components: an Nx30 matrix containing the log-Bayes factors on the basis of which the standard errors are computed

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify heteroskedasticity
sddr           = verify_volatility(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1) |>
  estimate(S = 10) |> 
  verify_volatility() -> sddr

Verifies heteroskedasticity of structural shocks equation by equation

Description

This function will be deprecated starting from version 4.0. It is replaced by verify_identification function.

Displays information that the model is homoskedastic.

Usage

## S3 method for class 'PosteriorBSVAR'
verify_volatility(posterior)

Arguments

posterior

the posterior element of the list from the estimation outcome

Value

Nothing. Just displays a message: The model is homoskedastic.

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify heteroskedasticity
sddr           = verify_volatility(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 10) |> 
  verify_volatility() -> sddr

Verifies heteroskedasticity of structural shocks equation by equation

Description

This function will be deprecated starting from version 4.0. It is replaced by verify_identification function.

H_0: \sigma^2_{n.1} = ... = \sigma^2_{n.M} = 1

log p(\omega_n = 0 | data) - log p(\omega_n = 0)

Therefore, a negative value of the difference is the evidence against homoskedasticity of the structural shock. The estimation of both elements of the difference requires numerical integration.

Usage

## S3 method for class 'PosteriorBSVARMIX'
verify_volatility(posterior)

Arguments

posterior

the posterior element of the list from the estimation outcome

Value

An object of class SDDRvolatility that is a list of three components:

logSDDR an N-vector with values of the logarithm of the Bayes factors for the homoskedasticity hypothesis for each of the shocks

components a list of three components for the computation of the Bayes factor

log_denominator: an N-vector with values of the logarithm of the Bayes factor denominators
log_numerator: an N-vector with values of the logarithm of the Bayes factor numerators
log_numerator_s: an NxS matrix of the log-full conditional posterior density ordinates computed to estimate the numerator
se_components: an Nx30 matrix containing the log-Bayes factors on the basis of which the standard errors are computed

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 1, M = 2)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify heteroskedasticity
sddr           = verify_volatility(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_mix$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  verify_volatility() -> sddr

Verifies heteroskedasticity of structural shocks equation by equation

Description

This function will be deprecated starting from version 4.0. It is replaced by verify_identification function.

H_0: \sigma^2_{n.1} = ... = \sigma^2_{n.M} = 1

log p(\omega_n = 0 | data) - log p(\omega_n = 0)

Therefore, a negative value of the difference is the evidence against homoskedasticity of the structural shock. The estimation of both elements of the difference requires numerical integration.

Usage

## S3 method for class 'PosteriorBSVARMSH'
verify_volatility(posterior)

Arguments

posterior

the posterior element of the list from the estimation outcome

Value

An object of class SDDRvolatility that is a list of three components:

logSDDR an N-vector with values of the logarithm of the Bayes factors for the homoskedasticity hypothesis for each of the shocks

components a list of three components for the computation of the Bayes factor

log_denominator: an N-vector with values of the logarithm of the Bayes factor denominators
log_numerator: an N-vector with values of the logarithm of the Bayes factor numerators
log_numerator_s: an NxS matrix of the log-full conditional posterior density ordinates computed to estimate the numerator
se_components: an Nx30 matrix containing the log-Bayes factors on the basis of which the standard errors are computed

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 1, M = 2)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify heteroskedasticity
sddr           = verify_volatility(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_msh$new(p = 1, M = 2) |>
  estimate(S = 10) |> 
  verify_volatility() -> sddr

Verifies heteroskedasticity of structural shocks equation by equation

Description

This function will be deprecated starting from version 4.0. It is replaced by verify_identification function.

H_0: \omega_n = 0

log p(\omega_n = 0 | data) - log p(\omega_n = 0)

Therefore, a negative value of the difference is the evidence against homoskedasticity of the structural shock. The estimation of both elements of the difference requires numerical integration.

Usage

## S3 method for class 'PosteriorBSVARSV'
verify_volatility(posterior)

Arguments

posterior

the posterior element of the list from the estimation outcome

Value

An object of class SDDRvolatility that is a list of three components:

logSDDR an N-vector with values of the logarithm of the Bayes factors for the homoskedasticity hypothesis for each of the shocks

components a list of three components for the computation of the Bayes factor

log_denominator: an N-vector with values of the logarithm of the Bayes factor denominators
log_numerator: an N-vector with values of the logarithm of the Bayes factor numerators
log_numerator_s: an NxS matrix of the log-full conditional posterior density ordinates computed to estimate the numerator
se_components: an Nx30 matrix containing the log-Bayes factors on the basis of which the standard errors are computed

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

Examples

# simple workflow
############################################################
# upload data
data(us_fiscal_lsuw)

# specify the model and set seed
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)
set.seed(123)

# estimate the model
posterior      = estimate(specification, 10)

# verify heteroskedasticity
sddr           = verify_volatility(posterior)

# workflow with the pipe |>
############################################################
set.seed(123)
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1) |>
  estimate(S = 10) |> 
  verify_volatility() -> sddr

Bayesian Estimation of Structural Vector Autoregressive Models

Description

Details

Note

Author(s)

References

See Also

Examples

Computes posterior draws of structural shock conditional standard deviations

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Computes posterior draws of structural shock conditional standard deviations

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Computes posterior draws of structural shock conditional standard deviations

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Computes posterior draws of structural shock conditional standard deviations

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Computes posterior draws of structural shock conditional standard deviations

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Computes posterior draws of structural shock conditional standard deviations

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Computes posterior draws from data predictive density

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Computes posterior draws from data predictive density

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Computes posterior draws from data predictive density

Description

Usage

Arguments

Value

Author(s)

See Also

Examples