Title:	High-Dimensional Temporal Disaggregation
Version:	2.0.0
Description:	First - Generates (potentially high-dimensional) high-frequency and low-frequency series for simulation studies in temporal disaggregation; Second - a toolkit utilizing temporal disaggregation and benchmarking techniques with a low-dimensional matrix of indicator series previously proposed in Dagum and Cholette (2006, ISBN:978-0-387-35439-2) ; and Third - novel techniques proposed by Mosley, Gibberd and Eckley (2021) <doi:10.48550/arXiv.2108.05783> for disaggregating low-frequency series in the presence of high-dimensional indicator matrices.
Imports:	Rdpack, zoo, lars, Matrix, withr
RdMacros:	Rdpack
License:	GPL (≥ 3)
Encoding:	UTF-8
RoxygenNote:	7.1.2
NeedsCompilation:	no
Packaged:	2022-05-17 22:52:06 UTC; kaveh
Author:	Luke Mosley [aut, cre], Kaveh S. Nobari [aut]
Maintainer:	Luke Mosley <l.mosley@lancaster.ac.uk>
Repository:	CRAN
Date/Publication:	2022-05-18 19:00:05 UTC

Function to generate an AR(1) variance-covariance matrix with parameter rho s.t. |rho| < 1.

Description

Function to generate an AR(1) variance-covariance matrix with parameter rho s.t. |rho| < 1.

Usage

ARcov(rho, n)

Function to generate an ARIMA(1,1,0) variance-covariance matrix for the Litterman method with parameter rho s.t. |rho| < 1.

Description

Function to generate an ARIMA(1,1,0) variance-covariance matrix for the Litterman method with parameter rho s.t. |rho| < 1.

Usage

ARcov_lit(rho, n)

High and Low-Frequency Data Generating Processes

Description

This function generates the high-frequency n \times 1 response vector y, according to y=X\beta+\epsilon, where X is an n\times p matrix of indicator series, and the p\times 1 coefficient vector may be sparse. The low-frequency n_l\times 1 vector Y can be generated by pre-multiplying an aggregation matrix n_l\times n matrix, such that the sum, the average, the last or the first value of y equates the corresponding Y observation. The parameter aggRatio is the specified aggregation ratio between the low and high frequency series, e.g. aggRatio = 4 for annual-to-quarterly and aggRatio = 3 for quarterly-to-monthly. If n > aggRatio \times n_l, then the last n - aggRatio \times n_l columns of the aggregation matrix are 0 such that Y is only observed up to n_l. For a comprehensive review, see Dagum and Cholette (2006).

Usage

TempDisaggDGP(
  n_l,
  n,
  aggRatio = 4,
  p = 1,
  beta = 1,
  sparsity = 1,
  method = "Chow-Lin",
  aggMat = "sum",
  rho = 0,
  mean_X = 0,
  sd_X = 1,
  sd_e = 1,
  simul = FALSE,
  setSeed = 42
)

Arguments

Value

y_Gen Generated high-frequency response series.

Y_Gen Generated low-frequency response series.

X_Gen Generated high-frequency indicator series.

Beta_Gen Generated coefficient vector.

e_Gen Generated high-frequency residual series.

References

Dagum EB, Cholette PA (2006). Benchmarking, temporal distribution, and reconciliation methods for time series, volume 186. Springer Science \& Business Media.

Examples

data = TempDisaggDGP(n_l=25, n=100, aggRatio=4,p=10, rho=0.5)
X = data$X_Gen
Y = data$Y_Gen

Function to do Chow-Lin temporal disaggregation from Chow and Lin (1971) and Litterman.

Description

Used in disaggregation.R to find estimates given the optimal rho parameter.

Usage

chowlin(Y, X, rho, aggMat, aggRatio, litterman = FALSE)

Arguments

Value

y Estimated high-frequency response series (n x 1 matrix).

betaHat Estimated coefficient vector (p x 1 matrix).

u_l Estimated aggregate residual series (n_l x 1 matrix).

References

Chow GC, Lin A (1971). “Best linear unbiased interpolation, distribution, and extrapolation of time series by related series.” The review of Economics and Statistics, 372–375.

Likelihood function from Chow-Lin or Litterman temporal disaggregation.

Description

Used in disaggregation.R to find estimates of the optimal rho parameter.

Usage

chowlin_likelihood(Y, X, vcov)

Arguments

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.

Temporal Disaggregation Methods

Description

This function contains the traditional standard-dimensional temporal disaggregation methods proposed by Denton (1971), Dagum and Cholette (2006), Chow and Lin (1971), Fernandez (1981) and Litterman (1983), and the high-dimensional methods of Mosley et al. (2021).

Usage

disaggregate(
  Y,
  X = matrix(data = rep(1, times = nrow(Y)), nrow = nrow(Y)),
  aggMat = "sum",
  aggRatio = 4,
  method = "Chow-Lin",
  Denton = "first"
)

Arguments

Details

Takes in a n_l x 1 low-frequency series to be disaggregated Y and a n x p high-frequency matrix of p indicator series X. If n > n_l x aggRatio where aggRatio is the aggregation ration (e.g. aggRatio = 4 if annual-to-quarterly disagg or aggRatio = 3 if quarterly-to-monthly disagg) then extrapolation is done to extrapolate up to n.

Value

y_Est Estimated high-frequency response series (n x 1 matrix).

beta_Est Estimated coefficient vector (p x 1 matrix).

rho_Est Estimated residual AR(1) autocorrelation parameter.

ul_Est Estimated aggregate residual series (n_l x 1 matrix).

References

Chow GC, Lin A (1971). “Best linear unbiased interpolation, distribution, and extrapolation of time series by related series.” The review of Economics and Statistics, 372–375.

Dagum EB, Cholette PA (2006). Benchmarking, temporal distribution, and reconciliation methods for time series, volume 186. Springer Science \& Business Media.

Denton FT (1971). “Adjustment of monthly or quarterly series to annual totals: an approach based on quadratic minimization.” Journal of the american statistical association, 66(333), 99–102.

Fernandez RB (1981). “A methodological note on the estimation of time series.” The Review of Economics and Statistics, 63(3), 471–476.

Litterman RB (1983). “A random walk, Markov model for the distribution of time series.” Journal of Business \& Economic Statistics, 1(2), 169–173.

Mosley L, Eckley I, Gibberd A (2021). “Sparse Temporal Disaggregation.” arXiv preprint arXiv:2108.05783.

Examples

data = TempDisaggDGP(n_l=25,n=100,p=10,rho=0.5)
X = data$X_Gen
Y = data$Y_Gen
fit_chowlin = disaggregate(Y=Y,X=X,method='Chow-Lin')
y_hat = fit_chowlin$y_Est

BIC score

Description

This function calculates the BIC score that has been shown to work better than ordinary BIC in high-dimensional scenarios. It uses the variance estimator given in Yu and Bien (2019).

Usage

hdBIC(X, Y, covariance, beta)

Arguments

References

Yu G, Bien J (2019). “Estimating the error variance in a high-dimensional linear model.” Biometrika, 106(3), 533–546.

Index of support for LARS algorithm when in high-dimensions

Description

This function prevents the support of beta becoming greater than n_l/2. This heuristic approach prevents erratic values of BIC when in high-dimensions.

Usage

k.index(matrix, n_l)

Refit LASSO estimate into GLS

Description

This function reduces the bias in LASSO estimates by re-fitting the support back into GLS.

Usage

refit(X, Y, beta)

Arguments

Function to do sparse temporal disaggregation from Mosley et al. (2021).

Description

Used in disaggregation.R to find estimates given the optimal rho parameter.

Usage

sptd(Y, X, rho, aggMat, aggRatio, adaptive = FALSE)

Arguments

Value

y Estimated high-frequency response series (n x 1 matrix).

betaHat Estimated coefficient vector (p x 1 matrix).

u_l Estimated aggregate residual series (n_l x 1 matrix).

References

Mosley L, Eckley I, Gibberd A (2021). “Sparse Temporal Disaggregation.” arXiv preprint arXiv:2108.05783.

Function to calculate the BIC score from sparse temporal disaggregation.

Description

Used in disaggregation.R to find estimates of the optimal rho parameter.

Usage

sptd_BIC(Y, X, vcov)

Arguments

References

There are no references for Rd macro ⁠\insertAllCites⁠ on this help page.