iAR: Irregularly Observed Autoregressive Models

Description

Description: Data sets, functions and scripts with examples to implement autoregressive models for irregularly observed time series. The models available in this package are the irregular autoregressive model (Eyheramendy et al.(2018) <doi:10.1093/mnras/sty2487>), the complex irregular autoregressive model (Elorrieta et al.(2019) <doi:10.1051/0004-6361/201935560>) and the bivariate irregular autoregressive model (Elorrieta et al.(2021) <doi:10.1093/mnras/stab1216>)

Details

"_PACKAGE"

'BiAR' Class

Description

Represents a bivariate irregular autoregressive (BiAR) time series model. This class extends the 'multidata' class and provides additional properties for modeling, forecasting, and interpolation of bivariate time series data.

Usage

BiAR(
  times = integer(0),
  series = integer(0),
  series_esd = integer(0),
  series_names = character(0),
  fitted_values = integer(0),
  loglik = integer(0),
  kalmanlik = integer(0),
  coef = c(0.8, 0),
  tAhead = 1,
  rho = 0,
  forecast = integer(0),
  interpolated_values = integer(0),
  interpolated_times = integer(0),
  interpolated_series = integer(0),
  zero_mean = TRUE,
  standardized = TRUE
)

Arguments

Details

The 'BiAR' class is designed to handle bivariate irregularly observed time series data using an autoregressive approach. It extends the 'multidata' class to include additional properties for modeling bivariate time series.

Key features of the 'BiAR' class include: - Support for bivariate time series data. - Forecasting and interpolation functionalities for irregular time points. - Assumptions of zero-mean and standardized processes, configurable by the user. - Estimation of model parameters and likelihoods, including Kalman likelihood.

Validation Rules

- '@times' must be a numeric vector without dimensions and strictly increasing. - '@series' must be a numeric matrix with two columns (bivariate) or be empty. - The number of rows in '@series' must match the length of '@times'. - '@series_esd', if provided, must be a numeric matrix. Its dimensions must match those of '@series', or it must have one row and the same number of columns. - If '@series_esd' contains NA values, they must correspond positionally to NA values in '@series'. - '@series_names', if provided, must be a character vector with length equal to the number of columns in '@series', and all names must be unique. - '@coef' must be a numeric vector of length 2, with each element strictly between -1 and 1. - '@tAhead' must be a strictly positive numeric scalar.

References

Elorrieta F, Eyheramendy S, Palma W, Ojeda C (2021). “A novel bivariate autoregressive model for predicting and forecasting irregularly observed time series.” Monthly Notices of the Royal Astronomical Society, 505(1), 1105-1116. ISSN 0035-8711, doi:10.1093/mnras/stab1216, https://academic.oup.com/mnras/article-pdf/505/1/1105/38391762/stab1216.pdf.

Examples

o=iAR::utilities()
o<-gentime(o, n=200, distribution = "expmixture", lambda1 = 130, lambda2 = 6.5,p1 = 0.15, p2 = 0.85)
times=o@times
my_BiAR <- BiAR(times = times,coef = c(0.9, 0.3), rho = 0.9)

# Access properties
my_BiAR@coef

'CiAR' Class

Description

Represents a complex irregular autoregressive (CiAR) time series model. This class extends the 'unidata' class and provides additional properties for modeling, forecasting, and interpolating irregularly observed time series data with both negative and positive autocorrelation.

Usage

CiAR(
  times = integer(0),
  series = integer(0),
  series_esd = integer(0),
  series_names = character(0),
  fitted_values = integer(0),
  kalmanlik = integer(0),
  coef = c(0.9, 0),
  tAhead = 1,
  forecast = integer(0),
  interpolated_values = integer(0),
  interpolated_times = integer(0),
  interpolated_series = integer(0),
  zero_mean = TRUE,
  standardized = TRUE
)

Arguments

Details

The 'CiAR' class is designed to handle irregularly observed time series data with either negative or positive autocorrelation using an autoregressive approach. It extends the 'unidata' class to include functionalities specific to the 'CiAR' model.

Key features of the 'CiAR' class include: - Support for irregularly observed time series data with negative or positive autocorrelation. - Forecasting and interpolation functionalities for irregular time points. - Configurable assumptions of zero-mean and standardized processes.

Validation

- Inherits all validation rules from the 'unidata' class: - '@times', '@series', and '@series_esd' must be numeric vectors. - '@times' must not contain 'NA' values and must be strictly increasing. - The length of '@series' must match the length of '@times'. - The length of '@series_esd' must be 0, 1, or equal to the length of '@series'. - 'NA' values in '@series' must correspond exactly (positionally) to 'NA' values in '@series_esd'. - '@series_names', if provided, must be a character vector of length 1.

- '@coef' must be a numeric vector of length 2 with no dimensions. - Each value in '@coef' must be in the interval [-1, 1]. - '@tAhead' must be a strictly positive numeric scalar.

References

Elorrieta, F, Eyheramendy, S, Palma, W (2019). “Discrete-time autoregressive model for unequally spaced time-series observations.” A&A, 627, A120. doi:10.1051/0004-6361/201935560.

Examples

o=iAR::utilities()
o<-gentime(o, n=200, distribution = "expmixture", lambda1 = 130, lambda2 = 6.5,p1 = 0.15, p2 = 0.85)
times=o@times
my_CiAR <- CiAR(times = times,coef = c(0.9, 0))

# Access properties
my_CiAR@coef

Transit of an extrasolar planet

Description

Time series corresponding to the residuals of the parametric model fitted by Jordan et al (2013) for a transit of an extrasolar planet.

Usage

Planets

Format

A data frame with 91 observations on the following 2 variables:

t

Time from mid-transit (hours).

r

Residuals of the parametric model fitted by Jordan et al (2013).

References

Jordán A, Espinoza N, Rabus M, Eyheramendy S, Sing D~K, Désert J, Bakos G~Á, Fortney J~J, López-Morales M, Maxted P~F~L, Triaud A~H~M~J, Szentgyorgyi A (2013). “A Ground-based Optical Transmission Spectrum of WASP-6b.” The Astrophysical Journal, 778, 184. doi:10.1088/0004-637X/778/2/184, 1310.6048.

Examples

data(Planets)
#plot(Planets[,1],Planets[,2],xlab='Time from mid-transit (hours)',ylab='Noise',pch=20)

Active Galactic Nuclei

Description

Time series of the AGN MCG-6-30-15 measured in the K-band between 2006 August and 2011 July with the ANDICAM camera mounted on the 1.3 m telescope at Cerro Tololo Inter-American Observatory (CTIO)

Usage

agn

Format

A data frame with 237 observations on the following 3 variables:

t

heliocentric Julian Day - 2450000

m

Flux $(10^(-15) ergs/s/cm^2 /A)$

merr

measurement error standard deviations.

References

Lira P, Arévalo P, Uttley P, McHardy IMM, Videla L (2015). “Long-term monitoring of the archetype Seyfert galaxy MCG-6-30-15: X-ray, optical and near-IR variability of the corona, disc and torus.” Monthly Notices of the Royal Astronomical Society, 454(1), 368-379. ISSN 0035-8711, doi:10.1093/mnras/stv1945.

Examples

data(agn)
plot(agn$t,agn$m,type="l",ylab="",xlab="")

Classical Cepheid

Description

Time series of a classical cepheid variable star obtained from HIPPARCOS.

Usage

clcep

Format

A data frame with 109 observations on the following 3 variables:

t

heliocentric Julian Day

m

magnitude

merr

measurement error of the magnitude (in mag).

Details

The frequency computed by GLS for this light curve is 0.060033386. Catalogs and designations of this star: HD 1989: HD 305996 TYCHO-2 2000:TYC 8958-2333-1 USNO-A2.0:USNO-A2 0225-10347916 HIP: HIP-54101

Examples

data(clcep)
f1=0.060033386
foldlc(clcep,f1)

ZTF g-band Cataclysmic Variable/Nova

Description

Time series of a cataclysmic variable/nova object observed in the g-band of the ZTF survey and processed by the ALeRCE broker.ZTF Object code: ZTF18aayzpbr

Usage

cvnovag

Format

A data frame with 67 observations on the following 3 variables:

t

heliocentric Julian Day - 2400000

m

magnitude

merr

measurement error standard deviations.

References

Förster F, Cabrera-Vives G, Castillo-Navarrete E, Estévez PA, Sánchez-Sáez P, Arredondo J, Bauer FE, Carrasco-Davis R, Catelan M, Elorrieta F, Eyheramendy S, Huijse P, Pignata G, Reyes E, Reyes I, Rodríguez-Mancini D, Ruz-Mieres D, Valenzuela C, Álvarez-Maldonado I, Astorga N, Borissova J, Clocchiatti A, Cicco DD, Donoso-Oliva C, Hernández-García L, Graham MJ, Jordán A, Kurtev R, Mahabal A, Maureira JC, Muñoz-Arancibia A, Molina-Ferreiro R, Moya A, Palma W, Pérez-Carrasco M, Protopapas P, Romero M, Sabatini-Gacitua L, Sánchez A, Martín JS, Sepúlveda-Cobo C, Vera E, Vergara JR (2021). “The Automatic Learning for the Rapid Classification of Events (ALeRCE) Alert Broker.” The Astronomical Journal, 161(5), 242. doi:10.3847/1538-3881/abe9bc.

Examples

data(cvnovag)
plot(cvnovag$t,cvnovag$m,type="l",ylab="",xlab="",col="green")

ZTF r-band Cataclysmic Variable/Nova

Description

Time series of a cataclysmic variable/nova object observed in the r-band of the ZTF survey and processed by the ALeRCE broker.ZTF Object code: ZTF18aayzpbr

Usage

cvnovar

Format

A data frame with 65 observations on the following 3 variables:

t

heliocentric Julian Day - 2400000

m

magnitude

merr

measurement error standard deviations.

References

Förster F, Cabrera-Vives G, Castillo-Navarrete E, Estévez PA, Sánchez-Sáez P, Arredondo J, Bauer FE, Carrasco-Davis R, Catelan M, Elorrieta F, Eyheramendy S, Huijse P, Pignata G, Reyes E, Reyes I, Rodríguez-Mancini D, Ruz-Mieres D, Valenzuela C, Álvarez-Maldonado I, Astorga N, Borissova J, Clocchiatti A, Cicco DD, Donoso-Oliva C, Hernández-García L, Graham MJ, Jordán A, Kurtev R, Mahabal A, Maureira JC, Muñoz-Arancibia A, Molina-Ferreiro R, Moya A, Palma W, Pérez-Carrasco M, Protopapas P, Romero M, Sabatini-Gacitua L, Sánchez A, Martín JS, Sepúlveda-Cobo C, Vera E, Vergara JR (2021). “The Automatic Learning for the Rapid Classification of Events (ALeRCE) Alert Broker.” The Astronomical Journal, 161(5), 242. doi:10.3847/1538-3881/abe9bc.

Examples

data(cvnovar)
plot(cvnovar$t,cvnovar$m,type="l",ylab="",xlab="",col="red")

Double Mode Cepheid.

Description

Time series of a double mode cepheid variable star obtained from OGLE.

Usage

dmcep

Format

A data frame with 191 observations on the following 3 variables:

t

heliocentric Julian Day

m

magnitude

merr

measurement error of the magnitude (in mag).

Details

The dominant frequency computed by GLS for this light curve is 0.7410152. The second frequency computed by GLS for this light curve is 0.5433353. OGLE-ID:175210

Examples

data(dmcep)
f1=0.7410152
foldlc(dmcep,f1)
#fit=harmonicfit(dmcep,f1)
#f2=0.5433353
#foldlc(cbind(dmcep$t,fit$res,dmcep$merr),f2)

Delta Scuti

Description

Time series of a Delta Scuti variable star obtained from HIPPARCOS.

Usage

dscut

Format

A data frame with 116 observations on the following 3 variables:

t

heliocentric Julian Day

m

magnitude

merr

measurement error of the magnitude (in mag).

Details

The frequency computed by GLS for this light curve is 14.88558646. Catalogs and designations of this star: HD 1989: HD 199757 TYCHO-2 2000: TYC 7973-401-1 USNO-A2.0: USNO-A2 0450-39390397 HIP: HIP 103684

Examples

data(dscut)
f1=14.88558646
foldlc(dscut,f1)

Eclipsing Binaries (Beta Lyrae)

Description

Time series of a Beta Lyrae variable star obtained from OGLE.

Usage

eb

Format

A data frame with 470 observations on the following 3 variables:

t

heliocentric Julian Day

m

magnitude

merr

measurement error of the magnitude (in mag).

Details

The frequency computed by GLS for this light curve is 1.510571586. Catalogs and designations of this star:OGLE051951.22-694002.7

Examples

data(eb)
f1=1.510571586
foldlc(eb,f1)

Fitted Values for iAR, CiAR, and BiAR Classes

Description

Fitted Values for the provided data. This method is implemented for: 1. Irregular Autoregressive models ('iAR') 2. Complex Irregular Autoregressive models ('CiAR') 3. Bivariate Autoregressive models ('BiAR')

Usage

fit(x, ...)

Arguments

Details

This method fits the specified time series model to the data contained in the object. Depending on the class of the input object:

• For iAR, the function supports three distribution families:

• "norm" for normal distribution.

• "t" for t-distribution.

• "gamma" for gamma distribution.

• For CiAR, the function uses complex autoregressive processes.

• For BiAR, the function fits a bivariate autoregressive process.

All required parameters (e.g., coefficients, time points) must be set before calling this method.

Value

An updated object of class iAR, CiAR, or BiAR, where the fitted_values property contains the fitted time series values.

References

Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.,Elorrieta, F, Eyheramendy, S, Palma, W (2019). “Discrete-time autoregressive model for unequally spaced time-series observations.” A&A, 627, A120. doi:10.1051/0004-6361/201935560.,Elorrieta F, Eyheramendy S, Palma W, Ojeda C (2021). “A novel bivariate autoregressive model for predicting and forecasting irregularly observed time series.” Monthly Notices of the Royal Astronomical Society, 505(1), 1105-1116. ISSN 0035-8711, doi:10.1093/mnras/stab1216, https://academic.oup.com/mnras/article-pdf/505/1/1105/38391762/stab1216.pdf.

Examples

# Example 1: Fitting a normal iAR model
library(iAR)
n=100
set.seed(6714)
o=iAR::utilities()
o<-gentime(o, n=n)
times=o@times
model_norm <- iAR(family = "norm", times = times, coef = 0.9)  
model_norm <- sim(model_norm)
model_norm <- kalman(model_norm) 
model_norm <- fit(model_norm)
plot(model_norm@times, model_norm@series, type = "l", main = "Original Series")
lines(model_norm@times, model_norm@fitted_values, col = "red", lwd = 2)
plot_fit(model_norm)

# Example 2: Fitting a CiAR model
set.seed(6714)
model_CiAR <- CiAR(times = times,coef = c(0.9, 0))
model_CiAR <- sim(model_CiAR)
y=model_CiAR@series
y1=y/sd(y)
model_CiAR@series=y1
model_CiAR@series_esd=rep(0,n)
model_CiAR <- kalman(model_CiAR)
print(model_CiAR@coef)
model_CiAR <- fit(model_CiAR)
yhat=model_CiAR@fitted_values

# Example 3: Fitting a BiAR model
n=80
set.seed(6714)
o=iAR::utilities()
o<-gentime(o, n=n)
times=o@times
model_BiAR <- BiAR(times = times,coef = c(0.9, 0.3), rho = 0.9)
model_BiAR <- sim(model_BiAR)
y=model_BiAR@series
y1=y/apply(y,2,sd)
model_BiAR@series=y1
model_BiAR@series_esd=matrix(0,n,2)
model_BiAR <- kalman(model_BiAR)
print(model_BiAR@coef) 
model_BiAR <- fit(model_BiAR)
print(model_BiAR@rho)
yhat=model_BiAR@fitted_values

Plotting folded light curves

Description

This function plots a time series folded on its period.

Usage

foldlc(file, f1, plot = TRUE)

Arguments

Value

A matrix whose first column has the folded (phased) observational times.

Examples

data(clcep)
f1=0.060033386
foldlc(clcep,f1)

Forecast for iAR, CiAR, and BiAR Classes

Description

Generates forecasts for the specified time series model. This method is implemented for: 1. Irregular Autoregressive models ('iAR') 2. Complex Irregular Autoregressive models ('CiAR') 3. Bivariate Autoregressive models ('BiAR')

Usage

forecast(x, ...)

Arguments

Details

This method generates forecasts for the specified time series model. Depending on the class of the input object:

• For iAR, the function supports three distribution families:

• "norm" for normal distribution.

• "t" for t-distribution.

• "gamma" for gamma distribution.

• For CiAR, the function uses complex autoregressive processes.

• For BiAR, the function generates forecasts for a bivariate autoregressive process.

All required parameters (e.g., coefficients, time points) must be set before calling this method.

Value

An updated object of class iAR, CiAR, or BiAR, where the forecast property contains the forecasted values.

References

Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.,Elorrieta, F, Eyheramendy, S, Palma, W (2019). “Discrete-time autoregressive model for unequally spaced time-series observations.” A&A, 627, A120. doi:10.1051/0004-6361/201935560.,Elorrieta F, Eyheramendy S, Palma W, Ojeda C (2021). “A novel bivariate autoregressive model for predicting and forecasting irregularly observed time series.” Monthly Notices of the Royal Astronomical Society, 505(1), 1105-1116. ISSN 0035-8711, doi:10.1093/mnras/stab1216, https://academic.oup.com/mnras/article-pdf/505/1/1105/38391762/stab1216.pdf.

Examples

# Example 1: Forecasting with a normal iAR model
library(iAR)
n=100
set.seed(6714)
o=iAR::utilities()
o<-gentime(o, n=n)
times=o@times
model_norm <- iAR(family = "norm", times = times, coef = 0.9)  
model_norm <- sim(model_norm)
model_norm <- kalman(model_norm) 
model_norm@tAhead=1.3
model_norm <- forecast(model_norm)
plot(times, model_norm@series, type = "l", main = "Original Series with Forecast")
points(max(times)+ model_norm@tAhead, model_norm@forecast, col = "blue", pch = 16)
plot_forecast(model_norm)

# Example 2: Forecasting with a CiAR model
set.seed(6714)
model_CiAR <- CiAR(times = times,coef = c(0.9, 0))
model_CiAR <- sim(model_CiAR)
y=model_CiAR@series
y1=y/sd(y)
model_CiAR@series=y1
model_CiAR@series_esd=rep(0,n)
model_CiAR <- kalman(model_CiAR)
print(model_CiAR@coef)
model_CiAR@tAhead=1.3
model_CiAR <-forecast(model_CiAR)
model_CiAR@forecast

# Example 3: Forecasting with a BiAR model
n=80
set.seed(6714)
o=iAR::utilities()
o<-gentime(o, n=n)
times=o@times
model_BiAR <- BiAR(times = times,coef = c(0.9, 0.3), rho = 0.9)
model_BiAR <- sim(model_BiAR)
y=model_BiAR@series
y1=y/apply(y,2,sd)
model_BiAR@series=y1
model_BiAR@series_esd=matrix(0,n,2)
model_BiAR <- kalman(model_BiAR)
print(model_BiAR@coef)
model_BiAR@tAhead=1.3
model_BiAR <-forecast(model_BiAR)
model_BiAR@forecast

Generating Irregularly spaced times

Description

A method for generating time points based on a statistical distribution. The results are stored in the 'times' slot of the 'utilities' object.

Usage

gentime(x, ...)

Arguments

Value

An updated 'utilities' object with the generated observation times stored in the 'times' slot.

References

Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.

Examples

set.seed(12917)
o1=iAR::utilities()
o1<-gentime(o1, n=200, distribution = "expmixture", lambda1 = 130, 
lambda2 = 6.5,p1 = 0.15, p2 = 0.85)
st=o1@times
mean(diff(st))

o1=iAR::utilities()
o1<-gentime(o1, n=200, distribution = "expmixture", lambda1 = 15, 
lambda2 = 2.5,p1 = 0.15, p2 = 0.85)
st=o1@times
mean(diff(st))

Harmonic Fit to Time Series

Description

This function fit an k-harmonic function to time series data.

Usage

harmonicfit(
  file,
  f1,
  nham = 4,
  weights = NULL,
  print = FALSE,
  remove_trend = TRUE
)

Arguments

Value

A list with the following components:

Examples

data(clcep)
f1=0.060033386
#results=harmonicfit(file=clcep[,1:2],f1=f1)
#results$R2
#results$MSE
#results=harmonicfit(file=clcep[,1:2],f1=f1,nham=3)
#results$R2
#results$MSE
#results=harmonicfit(file=clcep[,1:2],f1=f1,weights=clcep[,3])
#results$R2
#results$MSE

'iAR' Class

Description

Represents a univariate irregular autoregressive (iAR) time series model. This class extends the "unidata" class and includes additional properties for modeling, forecasting, and interpolation.

Usage

iAR(
  times = integer(0),
  series = integer(0),
  series_esd = integer(0),
  series_names = character(0),
  family = "norm",
  fitted_values = integer(0),
  loglik = integer(0),
  kalmanlik = integer(0),
  coef = 0.9,
  df = 3,
  sigma = 1,
  mean = 0,
  variance = 1,
  tAhead = 1,
  forecast = integer(0),
  interpolated_values = integer(0),
  interpolated_times = integer(0),
  interpolated_series = integer(0),
  zero_mean = TRUE,
  standardized = TRUE,
  hessian = FALSE,
  summary = list()
)

Arguments

Details

The 'iAR' class is designed to handle irregularly observed time series data using an autoregressive approach. It extends the "unidata" class to include additional modeling and diagnostic capabilities. Key functionalities include forecasting, interpolation, and model fitting.

The class also supports advanced modeling features, such as: - Different distribution families for the data (e.g., Gaussian, 't'-distribution). - Optional computation of the Hessian matrix for parameter estimation. - Standardized or zero-mean process assumptions.

Validation Rules

- Inherits all validation rules from the 'unidata' class: - '@times', '@series', and '@series_esd' must be numeric vectors. - '@times' must not contain 'NA' values and must be strictly increasing. - The length of '@series' must match the length of '@times'. - The length of '@series_esd' must be 0, 1, or equal to the length of '@series'. - 'NA' values in '@series' must correspond exactly (positionally) to 'NA' values in '@series_esd'. - '@series_names', if provided, must be a character vector of length 1.

- '@family' must be one of '"norm"', '"t"', or '"gamma"'. - '@coef' must be a numeric scalar strictly between 0 and 1. - '@df' must be a positive integer scalar **only if** 'family = "t"'; otherwise, it should not be specified. - '@sigma' must be a strictly positive numeric scalar (used in '"t"' family). - '@mean' and '@variance' must be strictly positive numeric scalars **only if** 'family = "gamma"'. - '@tAhead' must be a strictly positive numeric scalar.

References

Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.

Examples

# Create an `iAR` object
o=iAR::utilities()
o<-gentime(o, n=200, distribution = "expmixture", lambda1 = 130, lambda2 = 6.5,p1 = 0.15, p2 = 0.85)
times=o@times
my_iAR <- iAR(family = "norm", times = times, coef = 0.9,hessian=TRUE)

my_iAR@family
my_iAR@coef

Test for the significance of the autocorrelation estimated by the iAR package models

Description

This function perform a test for the significance of the autocorrelation estimated by the iAR package models. This test is based in to take N disordered samples of the original data.

Usage

iARPermutation(
  series,
  times,
  series_esd = 0,
  iter = 100,
  coef,
  model = "iAR",
  plot = TRUE,
  xlim = c(-1, 0),
  df = 3
)

Arguments

Details

The null hypothesis of the test is: The autocorrelation coefficient estimated for the time series belongs to the distribution of the coefficients estimated on the disordered data, which are assumed to be uncorrelated. Therefore, if the hypothesis is accepted, it can be concluded that the observations of the time series are uncorrelated.The statistic of the test is log(phi) which was contrasted with a normal distribution with parameters corresponding to the log of the mean and the variance of the phi computed for the N samples of the disordered data. This test differs for iARTest in that to perform this test it is not necessary to know the period of the time series.

Value

A list with the following components:

References

Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.

See Also

Planets,iARTest

Examples

data(Planets)
t<-Planets[,1]
res<-Planets[,2]
y=res/sqrt(var(res))
#res3=iARloglik(y,t,standardized=TRUE)[1]
#res3$coef
#set.seed(6713)
#require(ggplot2)
#test<-iARPermutation(series=y,times=t,coef=res3$coef,model="iAR",plot=TRUE,xlim=c(-9.6,-9.45))

Test for the significance of the autocorrelation estimated by the iAR package models in periodic irregularly observed time series

Description

This function perform a test for the significance of the autocorrelation estimated by the iAR package models. This test is based on the residuals of the periodical time series fitted with an harmonic model using an incorrect period.

Usage

iARTest(
  series,
  times,
  series_esd = 0,
  f,
  coef,
  model = "iAR",
  plot = TRUE,
  xlim = c(-1, 0),
  df = 3
)

Arguments

Details

The null hypothesis of the test is: The autocorrelation estimated in the time series belongs to the distribution of the coefficients estimated for the residuals of the data fitted using wrong periods. Therefore, if the hypothesis is rejected, it can be concluded that the residuals of the harmonic model do not remain a time dependency structure.The statistic of the test is log(phi) which was contrasted with a normal distribution with parameters corresponding to the log of the mean and the variance of the phi computed for the residuals of the bad fitted light curves.

Value

A list with the following components:

References

Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.

See Also

clcep, harmonicfit,iARPermutation

Examples

data(clcep)
f1=0.060033386
#results=harmonicfit(file=clcep,f1=f1)
#y=results$res/sqrt(var(results$res))
#st=results$t
#res3=iARloglik(y,st,standardized=TRUE)[1]
#res3$coef
#require(ggplot2)
#test<-iARTest(series=clcep[,2],times=clcep[,1],f=f1,coef=res3$coef,
#model="iAR",plot=TRUE,xlim=c(-10,0.5))
#test

Interpolation for iAR, CiAR, and BiAR Classes

Description

This method performs imputation of missing values in a time series using an autoregressive model. The imputation is done iteratively for each missing value, utilizing available data and model coefficients. Depending on the model family, the interpolation is performed differently: - For norm: A standard autoregressive model for normally distributed data. - For t: A model for time series with t-distributed errors. - For gamma: A model for time series with gamma-distributed errors. - For CiAR: A complex irregular autoregressive model. - For BiAR: A bivariate autoregressive model.

Usage

interpolation(x, ...)

Arguments

Details

Performs interpolation on time series with missing values. This method is implemented for: 1. Irregular Autoregressive models (iAR) 2. Complex Irregular Autoregressive models (CiAR) 3. Bivariate Autoregressive models (BiAR)

The method handles missing values (NA) in the time series by imputing them iteratively. For each missing value, the available data is used to fit the autoregressive model, and the missing value is imputed based on the model's output. For the CiAR and BiAR models, the error standard deviations and initial values are also considered during imputation.

Value

An object of the same class as x with interpolated time series.

References

Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.,Elorrieta, F, Eyheramendy, S, Palma, W (2019). “Discrete-time autoregressive model for unequally spaced time-series observations.” A&A, 627, A120. doi:10.1051/0004-6361/201935560.,Elorrieta F, Eyheramendy S, Palma W, Ojeda C (2021). “A novel bivariate autoregressive model for predicting and forecasting irregularly observed time series.” Monthly Notices of the Royal Astronomical Society, 505(1), 1105-1116. ISSN 0035-8711, doi:10.1093/mnras/stab1216, https://academic.oup.com/mnras/article-pdf/505/1/1105/38391762/stab1216.pdf.

See Also

forecast for forecasting methods for these models.

Examples

# Interpolation for iAR model
library(iAR)
n=100
set.seed(6714)
o=iAR::utilities()
o<-gentime(o, n=n)
times=o@times
model_norm <- iAR(family = "norm", times = times, coef = 0.9)  
model_norm <- sim(model_norm)
y=model_norm@series
y1=y/sd(y)
model_norm@series=y1
model_norm@series_esd=rep(0,n)
model_norm <- kalman(model_norm) 
print(model_norm@coef)
napos=10
model_norm@series[napos]=NA
model_norm <- interpolation(model_norm)
interpolation=na.omit(model_norm@interpolated_values)
mse=as.numeric(y1[napos]-interpolation)^2
print(mse)
plot(times,y,type='l',xlim=c(times[napos-5],times[napos+5]))
points(times,y,pch=20)
points(times[napos],interpolation*sd(y),col="red",pch=20)

# Interpolation for CiAR model
model_CiAR <- CiAR(times = times,coef = c(0.9, 0))
model_CiAR <- sim(model_CiAR)
y=model_CiAR@series
y1=y/sd(y)
model_CiAR@series=y1
model_CiAR@series_esd=rep(0,n)
model_CiAR <- kalman(model_CiAR)
print(model_CiAR@coef)
napos=10
model_CiAR@series[napos]=NA
model_CiAR <- interpolation(model_CiAR)
interpolation=na.omit(model_CiAR@interpolated_values)
mse=as.numeric(y1[napos]-interpolation)^2
print(mse)
plot(times,y,type='l',xlim=c(times[napos-5],times[napos+5]))
points(times,y,pch=20)
points(times[napos],interpolation*sd(y),col="red",pch=20)
# Interpolation for BiAR model
model_BiAR <- BiAR(times = times,coef = c(0.9, 0.3), rho = 0.9)
model_BiAR <- sim(model_BiAR)
y=model_BiAR@series
y1=y/apply(y,2,sd)
model_BiAR@series=y1
model_BiAR@series_esd=matrix(0,n,2)
model_BiAR <- kalman(model_BiAR)
print(model_BiAR@coef) 
napos=10
model_BiAR@series[napos,1]=NA
model_BiAR@series_esd[napos,1]=NA
model_BiAR <- interpolation(model_BiAR)
interpolation=na.omit(model_BiAR@interpolated_values[,1])
mse=as.numeric(y1[napos,1]-interpolation)^2
print(mse)
par(mfrow=c(2,1))
plot(times,y[,1],type='l',xlim=c(times[napos-5],times[napos+5]))
points(times,y[,1],pch=20)
points(times[napos],interpolation*apply(y,1,sd)[1],col="red",pch=20)
plot(times,y[,2],type='l',xlim=c(times[napos-5],times[napos+5]))
points(times,y[,2],pch=20)

Maximum Likelihood Estimation of Parameters for iAR, CiAR, and BiAR Models using the Kalman Filter

Description

Performs Maximum Likelihood Estimation (MLE) of the parameters of the iAR, CiAR, and BiAR models by maximizing the likelihood function using the Kalman filter. This method applies the Kalman filter to compute the likelihood and estimate the model parameters that maximize the likelihood for each model type.

Usage

kalman(x, ...)

Arguments

Details

This function applies the Kalman filter to perform Maximum Likelihood Estimation (MLE) of the parameters of the autoregressive models (iAR, CiAR, BiAR). The Kalman filter is used to maximize the likelihood function based on the given time series data, and the parameters that maximize the likelihood are estimated.

- For iAR, the Kalman filter is applied to estimate the model parameters by maximizing the likelihood. - For CiAR, the Kalman filter is applied to estimate the parameters of the complex autoregressive model by maximizing the likelihood. - For BiAR, the Kalman filter is applied to estimate the parameters of the bivariate autoregressive model by maximizing the likelihood.

The method returns the updated model object, including the estimated parameters and the log-likelihood value.

Value

An updated object of class iAR, CiAR, or BiAR, where the coef property is updated with the estimated model parameters (using MLE) and the kalmanlik property contains the log-likelihood value of the model.

References

Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.,Elorrieta, F, Eyheramendy, S, Palma, W (2019). “Discrete-time autoregressive model for unequally spaced time-series observations.” A&A, 627, A120. doi:10.1051/0004-6361/201935560.,Elorrieta F, Eyheramendy S, Palma W, Ojeda C (2021). “A novel bivariate autoregressive model for predicting and forecasting irregularly observed time series.” Monthly Notices of the Royal Astronomical Society, 505(1), 1105-1116. ISSN 0035-8711, doi:10.1093/mnras/stab1216, https://academic.oup.com/mnras/article-pdf/505/1/1105/38391762/stab1216.pdf.

Examples

# Example 1: Applying Kalman filter for MLE of iAR model parameters
library(iAR)
n=100
set.seed(6714)
o=iAR::utilities()
o<-gentime(o, n=n)
times=o@times
model_norm <- iAR(family = "norm", times = times, coef = 0.9,hessian=TRUE)
model_norm <- sim(model_norm)
model_norm <- kalman(model_norm)  
print(model_norm@coef)  # Access the estimated coefficients
print(model_norm@kalmanlik)  # Access the Kalman likelihood value

# Example 2: Applying Kalman filter for MLE of CiAR model parameters
set.seed(6714)
model_CiAR <- CiAR(times = times,coef = c(0.9, 0))
model_CiAR <- sim(model_CiAR)
y=model_CiAR@series
y1=y/sd(y)
model_CiAR@series=y1
model_CiAR@series_esd=rep(0,n)
model_CiAR <- kalman(model_CiAR)
print(model_CiAR@coef)
print(model_CiAR@kalmanlik)  

# Example 3: Applying Kalman filter for MLE of BiAR model parameters
set.seed(6714)
model_BiAR <- BiAR(times = times,coef = c(0.9, 0.3), rho = 0.9)
model_BiAR <- sim(model_BiAR)
y=model_BiAR@series
y1=y/apply(y,2,sd)
model_BiAR@series=y1
model_BiAR@series_esd=matrix(0,n,2)
model_BiAR <- kalman(model_BiAR)
print(model_BiAR@coef) 
print(model_BiAR@kalmanlik)  

Maximum Likelihood Estimation for iAR Models

Description

Maximum Likelihood Estimation for irregular autoregressive (iAR) models, supporting different distribution families: normal ('iAR'), t ('iAR-T'), and gamma ('iAR-Gamma').

Usage

loglik(x, ...)

Arguments

Details

This method estimates the parameters of an iAR model using the Maximum Likelihood Estimation (MLE) approach. Depending on the chosen distribution family, the corresponding likelihood function is maximized:

• "norm" maximizes the likelihood for a normally-distributed series.

• "t" maximizes the likelihood for a t-distributed series.

• "gamma" maximizes the likelihood for a gamma-distributed series.

The function updates the iAR object with the estimated parameters, the log-likelihood value, and a summary table that includes standard errors and p-values.

Value

An updated iAR object with the following additional attributes:

• coef: Estimated model coefficients.

• loglik: Log-likelihood value of the model.

• summary: A summary table containing parameter estimates, standard errors, and p-values.

• sigma: For t and gamma families, the estimated scale parameter.

• mean: For the gamma family, the estimated mean parameter.

• variance: For the gamma family, the estimated variance parameter.

References

Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.

Examples

# Example: Estimating parameters for a normal iAR model
library(iAR)
times <- 1:100
model <- iAR(family = "norm", times = times, coef = 0.9, hessian = TRUE)
model <- sim(model)  # Simulate the series
model <- loglik(model)  # Estimate parameters using MLE
print(model@coef)  # Access the estimated coefficients
print(model@loglik)  # Access the computed log-likelihood

Multidata Class

Description

The 'multidata' class is an S7 class designed to represent multidimensional time series models, including the main time series and additional series (e.g., error standard deviations or related variables).

Usage

multidata(
  times = integer(0),
  series = integer(0),
  series_esd = integer(0),
  series_names = character(0)
)

Arguments

Validation Rules

- '@times' must be a numeric vector and strictly increasing. - '@series' must be a numeric matrix or empty. Its number of rows must match the length of '@times'. - '@series_esd' must be a numeric matrix or empty. If provided and not empty, its dimensions must match those of '@series'. - If '@series_names' is provided, it must be a character vector of the same length as the number of columns of '@series', and contain unique values.

See Also

[BiAR]

Examples

# Create a multidata object
multidata_instance <- multidata(
  times = c(1, 2, 3, 4),
  series = matrix(c(10, 20, 15, 25,
                    12, 18, 17, 23), 
                  nrow = 4, ncol = 2),
  series_esd = matrix(c(1, 1.5, 1.2, 1.8,
                        0.9, 1.3, 1.1, 1.7),
                      nrow = 4, ncol = 2)
)

Pairing two irregularly observed time series

Description

This method pairs the observational times of two irregularly observed time series.

Usage

pairingits(x, ...)

Arguments

Details

The method checks the observational times in both input time series and pairs the measurements if they fall within the specified tolerance ('tol'). If a measurement in one series cannot be paired, it is filled with 'NA' values for the corresponding columns of the other series.

Value

An object of class 'utilities' with two slots:

References

Elorrieta F, Eyheramendy S, Palma W, Ojeda C (2021). “A novel bivariate autoregressive model for predicting and forecasting irregularly observed time series.” Monthly Notices of the Royal Astronomical Society, 505(1), 1105-1116. ISSN 0035-8711, doi:10.1093/mnras/stab1216, https://academic.oup.com/mnras/article-pdf/505/1/1105/38391762/stab1216.pdf.

Examples

data(cvnovag)
data(cvnovar)
datag=cvnovag
datar=cvnovar
o1=iAR::utilities()
o1<-pairingits(o1, datag,datar,tol=0.1)
pargr1=na.omit(o1@paired)
st=apply(pargr1[,c(1,4)],1,mean)
model_BiAR <- BiAR(times = st,series=pargr1[,c(2,5)],series_esd=pargr1[,c(3,6)])
model_BiAR <- kalman(model_BiAR)

Plot Method for unidata Objects

Description

This method allows visualizing 'unidata' and 'multidata' objects using the 'plot.zoo' function from the 'zoo' package. It converts the 'unidata' ('multidata') object into a 'zoo' object and then applies the plotting function to the time series contained in the object.

Arguments

Plot Fit Method for unidata Objects

Description

This method visualizes the 'unidata' and 'multidata' objects by plotting both the original time series and the fitted values. The 'unidata' ('multidata') object is converted into a 'zoo' object for plotting, and the fitted values are added as a secondary line with a different style and color.

Usage

plot_fit(x,...)

Arguments

Plot Forecast Method for unidata Objects

Description

This method visualizes the 'unidata' and 'multidata' objects by plotting both the original time series and the forecasted values. The 'unidata' ('multidata') object is converted into a 'zoo' object for plotting, and the forecasted values are added as points with a different color.

Usage

plot_forecast(x,...)

Arguments

Simulate Time Series for Multiple iAR Models

Description

Simulates a time series for irregular autoregressive (iAR) models, including: 1. Normal iAR model ('iAR') 2. T-distribution iAR model ('iAR-T') 3. Gamma-distribution iAR model ('iAR-Gamma')

Usage

sim(x, ...)

Arguments

Details

This function simulates time series based on the specified model and its parameters. Depending on the class of the input object:

• For iAR models, it supports three distribution families:

• "norm" for normal distribution.

• "t" for t-distribution.

• "gamma" for gamma distribution.

• For CiAR models, it uses complex autoregressive processes to generate the time series.

• For BiAR models, it simulates a BiAR process using specified coefficients and correlation.

The coefficients and any family-specific parameters must be set before calling this function.

Value

An updated object of class iAR, CiAR, or BiAR, where the series property contains the simulated time series.

References

Eyheramendy S, Elorrieta F, Palma W (2018). “An irregular discrete time series model to identify residuals with autocorrelation in astronomical light curves.” Monthly Notices of the Royal Astronomical Society, 481(4), 4311-4322. ISSN 0035-8711, doi:10.1093/mnras/sty2487, https://academic.oup.com/mnras/article-pdf/481/4/4311/25906473/sty2487.pdf.,Elorrieta, F, Eyheramendy, S, Palma, W (2019). “Discrete-time autoregressive model for unequally spaced time-series observations.” A&A, 627, A120. doi:10.1051/0004-6361/201935560.,Elorrieta F, Eyheramendy S, Palma W, Ojeda C (2021). “A novel bivariate autoregressive model for predicting and forecasting irregularly observed time series.” Monthly Notices of the Royal Astronomical Society, 505(1), 1105-1116. ISSN 0035-8711, doi:10.1093/mnras/stab1216, https://academic.oup.com/mnras/article-pdf/505/1/1105/38391762/stab1216.pdf.

Examples

# Example 1: Simulating a normal iAR model
library(iAR)
n=100
set.seed(6714)
o=iAR::utilities()
o<-gentime(o, n=n)
times=o@times
model_norm <- iAR(family = "norm", times = times, coef = 0.9,hessian=TRUE)
model_norm <- sim(model_norm)
plot(model_norm, type = "l", main = "Simulated iAR-Norm Series")

# Example 2: Simulating a CiAR model
set.seed(6714)
model_CiAR <- CiAR(times = times,coef = c(0.9, 0))
model_CiAR <- sim(model_CiAR)
plot(model_CiAR , type = "l", main = "Simulated CiAR Series")

# Example 3: Simulating a BiAR model
set.seed(6714)
model_BiAR <- BiAR(times = times,coef = c(0.9, 0.3), rho = 0.9)
model_BiAR <- sim(model_BiAR)
plot(times, model_BiAR@series[,1], type = "l", main = "Simulated BiAR Series")

Summary Method for unidata Objects

Description

This method provides a summary of the 'unidata' object, which represents an iAR (irregular autoregressive) model. The summary includes information about the model family (e.g., "normal", "t", "gamma"), the coefficients, standard errors, t-values, and p-values. The output is formatted to display the relevant statistics based on the model family.

Arguments

Unidata Class

Description

The 'unidata' class is an S7 class designed to represent univariate irregularly observed time series models with associated times, values, and optional error standard deviations.

Usage

unidata(
  times = integer(0),
  series = integer(0),
  series_esd = integer(0),
  series_names = character(0)
)

Arguments

Validation Rules

- '@times', '@series', and '@series_esd' must be numeric vectors. - '@times' must not contain 'NA' values and must be strictly increasing. - The length of '@series' must match the length of '@times'. - The length of '@series_esd' must be 0, 1, or equal to the length of '@series'. - 'NA' values in '@series' must correspond exactly (positionally) to 'NA' values in '@series_esd'. - '@series_names', if provided, must be a character vector of length 1.

See Also

[iAR], [CiAR]

Examples

# Create a unidata object
unidata_instance <- unidata(
  times = c(1, 2, 3, 4),
  series = c(10, 20, 15, 25),
  series_esd = c(1, 1.5, 1.2, 1.8),
  series_names = "my_series")

Utilities Class

Description

The 'utilities' class is an S7 class designed to group utility functions that are not directly tied to other specific objects in the package. These include the functions 'gentime', 'paringits', 'harmonicfit', and 'foldlc'.

Usage

utilities(
  times = integer(0),
  series = integer(0),
  series_esd = integer(0),
  paired = integer(0)
)

Arguments

Description

This class acts as a container for standalone methods that perform independent operations within the package. By grouping them under a single class, the package achieves better modularity and organization, facilitating maintenance and extensibility.

Available Methods

- 'gentime': Generates time points based on a specified statistical distribution. - 'paringits': A method for pairing irregular time series. - 'harmonicfit': A method for fitting harmonic models to data. - 'foldlc': A method for folding light curves in time series analysis.

Examples

# Create a utilities object