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, and include exclusion restrictions on autoregressive parameters. 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 (2025) <doi:10.48550/arXiv.2410.15090> complement all this. The implemented techniques align closely with those presented in Lütkepohl, Shang, Uzeda, & Woźniak (2025) <doi:10.1016/j.jeconom.2025.106107>, Lütkepohl & Woźniak (2020) <doi:10.1016/j.jedc.2020.103862>, and Song & Woźniak (2021) <doi:10.1093/acrefore/9780190625979.013.174> and they embed many popular models proposed by other authors. The 'bsvars' package is aligned regarding objects, workflows, and code structure with the R packages 'bsvarSIGNs' by Wang & Woźniak (2025) <doi:10.32614/CRAN.package.bsvarSIGNs>, 'bvars' by Liu, Ramirez Hassan, Woźniak (2026) <doi:10.32614/CRAN.package.bvars>, and 'bpvars' by Woźniak (2026) <doi:10.32614/CRAN.package.bpvars>, and they constitute an integrated toolset.
Version:	4.0
Date:	2026-08-19
Maintainer:	Tomasz Woźniak <wozniak.tom@pm.me>
Depends:	R (≥ 4.1.0)
Imports:	Rcpp (≥ 1.0.7), RcppProgress (≥ 0.1), RcppTN, GIGrvg, R6, stochvol, generics
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
Config/roxygen2/version:	8.0.0
NeedsCompilation:	yes
Packaged:	2026-08-22 05:21:04 UTC; twozniak
Author:	Tomasz Woźniak [aut, cre], Fei Shang [ctb] (co-authored the Journal of Econometrics methodological paper by Lütkepohl, Shang, Uzeda, Woźniak (2026), introduced major code corrections and improvements), Helmut Lütkepohl [ctb] (co-authored the Journal of Econometrics methodological paper by Lütkepohl, Shang, Uzeda, Woźniak (2026)), Luis Uzeda [ctb] (co-authored the Journal of Econometrics methodological paper by Lütkepohl, Shang, Uzeda, Woźniak (2026)), Xiaolei Wang [ctb] (corrected C++ code for historical decompositions), Bruno Cavalcante [ctb] (corrected R code for HMSH forecasting)
Repository:	CRAN
Date/Publication:	2026-08-22 16:00:17 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, and include exclusion restrictions on autoregressive parameters. 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 (2025) <doi:10.48550/arXiv.2410.15090> complement all this. The implemented techniques align closely with those presented in Lütkepohl, Shang, Uzeda, & Woźniak (2025) <doi:10.1016/j.jeconom.2025.106107>, Lütkepohl & Woźniak (2020) <doi:10.1016/j.jedc.2020.103862>, and Song & Woźniak (2021) <doi:10.1093/acrefore/9780190625979.013.174> and they embed many popular models proposed by other authors. The 'bsvars' package is aligned regarding objects, workflows, and code structure with the R packages 'bsvarSIGNs' by Wang & Woźniak (2025) <doi:10.32614/CRAN.package.bsvarSIGNs>, 'bvars' by Liu, Ramirez Hassan, Woźniak (2026) <doi:10.32614/CRAN.package.bvars>, and 'bpvars' by Woźniak (2026) <doi:10.32614/CRAN.package.bpvars>, 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 assumptions regarding the structural shocks U, namely, temporal and contemporaneous independence. They imply 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 non-centred Stochastic Volatility process for variances

• heteroskedastic model with centred Stochastic Volatility process for variances

• heteroskedastic model with stationary Markov switching in the variances

• heteroskedastic model with sparse Markov switching in the variances where the number of heteroskedastic components is estimated

• heteroskedastic model with stationary heterogeneous Markov switching in the variances, where each shock volatility has its own Markov process

• heteroskedastic model with sparse heterogeneous Markov switching in the variances where the number of heteroskedastic components is estimated

• heteroskedastic model with exogenous heteroskedastic regime changes in the variances

• a model with Student-t distributed structural shocks with estimated equation-specific degrees-of-freedom parameter

• non-normal model with a finite mixture of normal components and component-specific variances

• non-normal model with a sparse mixture of normal components and component-specific variances where the number of heteroskedastic components is estimated

The structural shocks can be either normally or Student-t distributed, where in the latter case the shock-specific degrees of freedom parameters are 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 estimation follows closely Lütkepohl, Shang, Uzeda, & Woźniak (2025). 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 identification problems are considered in Lütkepohl, Shang, Uzeda, & Woźniak (2025) and Lütkepohl & Woźniak (2020).

Identification verification. The structural shocks can be identified through heteroskedasticity or non-normality following Lütkepohl, Shang, Uzeda, & Woźniak (2025) and Lütkepohl & Woźniak (2020). The package provides functions to verify both, homoskedasticity and normality of the structural shocks, which facilitates making probabilistic statements regarding the identification. Additionally, the package makes it possible to verify linear restrictions on autoregressive parameters.

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.

Liu, Ramirez Hassan, Woźniak (2026) bvars: Bayesian Forecasting with Large Vector Autoregressions. R package version 1.0, doi:10.32614/CRAN.package.bvars.

Lütkepohl, H., Shang, F., Uzeda, L., and Woźniak, T. (2025) Partial identification of structural vector autoregressions with non-centred stochastic volatility. Journal of Econometrics 256, 106107, doi:10.1016/j.jeconom.2025.106107.

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.

Wang X, Woźniak T (2025). bsvarSIGNs: Bayesian SVARs with Sign, Zero, and Narrative Restrictions. R package version 2.0, doi:10.32614/CRAN.package.bsvarSIGNs.

Woźniak T (2026) bpvars: Forecasting with Bayesian Panel Vector Autoregressions. R package version 2.0, doi:10.32614/CRAN.package.bpvars.

See Also

Useful links:

• https://bsvars.org/bsvars/

• Report bugs at https://github.com/bsvars/bsvars/issues

Examples

spec  = specify_bsvar_sv$new(         # specify the model
          us_fiscal_lsuw, 
          exogenous = us_fiscal_ex
        )
burn  = estimate(spec, 5)             # run the burn-in
post  = estimate(burn, 5)             # estimate the model
irf   = compute_impulse_responses(    # compute impulse responses
          post, 
          horizon = 2
         )

# compute forecast error variance decomposition one year ahead
fevd  = compute_variance_decompositions(post, horizon = 4)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_sv$new(exogenous = us_fiscal_ex) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  compute_variance_decompositions(horizon = 4) -> fevds

# conditional forecasting using a model with exogenous variables
############################################################
us_fiscal_lsuw |>
  specify_bsvar_sv$new(exogenous = us_fiscal_ex) |>
  estimate(S = 5) |> 
  estimate(S = 5) -> post
  
 post |> forecast(
    horizon = 8,
    exogenous_forecast = us_fiscal_ex_forecasts,
    conditional_forecast = us_fiscal_cond_forecasts
  ) -> pred
  
  pred |> summary()
  pred |> plot(probability = 0.68)
  
# estimation of a model with exogeneity restrictions on the  autoregressive matrix
#############################################################
A = matrix(TRUE, 3, 7)
A[1,3] = A[1,6] = FALSE
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 2, A = A) |>
  estimate(S = 5) |> 
  estimate(S = 5) -> post
post |> summary()

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

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

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)
sigma          = compute_conditional_sd(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)
sigma          = compute_conditional_sd(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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 'PosteriorBSVAREXH'
compute_conditional_sd(posterior)

Arguments

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

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_exh$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)
csd     = compute_conditional_sd(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_exh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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 'PosteriorBSVARHMSH'
compute_conditional_sd(posterior)

Arguments

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

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_hmsh$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)
csd     = compute_conditional_sd(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_hmsh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_mix$new(us_fiscal_lsuw, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)
csd     = compute_conditional_sd(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_mix$new(M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_msh$new(us_fiscal_lsuw, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)
csd     = compute_conditional_sd(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_msh$new(M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_sv$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)
csd     = compute_conditional_sd(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_sv$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_t$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)
csd     = compute_conditional_sd(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_t$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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

See Also

estimate, summary

Examples

specification  = specify_bsvar$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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

See Also

estimate, summary

Examples

specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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 'PosteriorBSVAREXH'
compute_fitted_values(posterior)

Arguments

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

See Also

estimate, summary

Examples

specification  = specify_bsvar_exh$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_exh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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 'PosteriorBSVARHMSH'
compute_fitted_values(posterior)

Arguments

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

See Also

estimate, summary

Examples

specification  = specify_bsvar_hmsh$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_hmsh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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 'PosteriorBSVARMIX'
compute_fitted_values(posterior)

Arguments

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

See Also

estimate, summary

Examples

specification  = specify_bsvar_mix$new(us_fiscal_lsuw, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_mix$new(M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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

See Also

estimate, summary

Examples

specification  = specify_bsvar_msh$new(us_fiscal_lsuw, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_msh$new(M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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

See Also

estimate, summary

Examples

specification  = specify_bsvar_sv$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_sv$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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

See Also

estimate, summary

Examples

specification  = specify_bsvar_t$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_t$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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 and Xiaolei Wang adamwang15@gmail.com

References

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

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar$new(diff(us_fiscal_lsuw))
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# compute historical decompositions
hd            = compute_historical_decompositions(posterior)

# workflow with the pipe |>
############################################################
diff(us_fiscal_lsuw) |>
  specify_bsvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  compute_historical_decompositions() -> hd

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

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

Arguments

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.

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar$new(diff(us_fiscal_lsuw))
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# compute historical decompositions
hd            = compute_historical_decompositions(posterior)

# workflow with the pipe |>
############################################################
diff(us_fiscal_lsuw) |>
  specify_bsvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  compute_historical_decompositions() -> hd
  

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

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

Arguments

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.

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_exh$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# compute historical decompositions
hd             = compute_historical_decompositions(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_exh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  compute_historical_decompositions() -> hds
  

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

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

Arguments

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.

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_hmsh$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# compute historical decompositions
hd             = compute_historical_decompositions(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_hmsh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  compute_historical_decompositions() -> hds
  

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

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

Arguments

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.

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_mix$new(us_fiscal_lsuw, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# compute historical decompositions
hd             = compute_historical_decompositions(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_mix$new(M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  compute_historical_decompositions() -> hds
  

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

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

Arguments

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.

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_msh$new(us_fiscal_lsuw, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# compute historical decompositions
hd             = compute_historical_decompositions(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_msh$new(M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  compute_historical_decompositions() -> hds
  

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

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

Arguments

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.

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# compute historical decompositions
hd             = compute_historical_decompositions(posterior)

# workflow with the pipe |>
############################################################
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

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

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

Arguments

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.

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_t$new(diff(us_fiscal_lsuw))
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# compute historical decompositions
hd            = compute_historical_decompositions(posterior)

# workflow with the pipe |>
############################################################
diff(us_fiscal_lsuw) |>
  specify_bsvar_t$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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.

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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.

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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 'PosteriorBSVAREXH'
compute_impulse_responses(posterior, horizon, standardise = FALSE)

Arguments

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.

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_exh$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_exh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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 'PosteriorBSVARHMSH'
compute_impulse_responses(posterior, horizon, standardise = FALSE)

Arguments

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.

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_hmsh$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_msh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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 'PosteriorBSVARMIX'
compute_impulse_responses(posterior, horizon, standardise = FALSE)

Arguments

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.

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 1, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_mix$new(p = 1, M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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.

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 1, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_msh$new(p = 1, M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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.

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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.

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_t$new(us_fiscal_lsuw, p = 1)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_t$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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.

See Also

estimate, summary

Examples

specification  = specify_bsvar_msh$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# 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 |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_msh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) -> posterior
regimes        = compute_regime_probabilities(posterior)
filtered       = compute_regime_probabilities(posterior, "filtered")

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

## S3 method for class 'PosteriorBSVAREXH'
compute_regime_probabilities(posterior, type = "realized")

Arguments

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.

See Also

estimate, summary

Examples

specification  = specify_bsvar_msh$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# 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 |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_msh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) -> posterior
regimes        = compute_regime_probabilities(posterior)
filtered       = compute_regime_probabilities(posterior, "filtered")

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

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

Arguments

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.

See Also

estimate, summary

Examples

specification  = specify_bsvar_hmsh$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# 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 |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_hmsh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) -> posterior
regimes        = compute_regime_probabilities(posterior)
filtered       = compute_regime_probabilities(posterior, "filtered")

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

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

Arguments

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.

See Also

estimate, summary

Examples

specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 2, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# 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 |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_mix$new(p = 1, M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) -> posterior
regimes        = compute_regime_probabilities(posterior)
filtered       = compute_regime_probabilities(posterior, "filtered")

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

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

Arguments

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.

See Also

estimate, summary

Examples

specification  = specify_bsvar_msh$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# 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 |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_msh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) -> 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

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

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# compute structural shocks
shocks         = compute_structural_shocks(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# compute structural shocks
shocks         = compute_structural_shocks(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  compute_structural_shocks() -> ss

Computes posterior draws of structural shocks

Description

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

Usage

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

Arguments

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

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_exh$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# compute structural shocks
shocks         = compute_structural_shocks(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_exh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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 'PosteriorBSVARHMSH'
compute_structural_shocks(posterior)

Arguments

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

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_hmsh$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# compute structural shocks
shocks         = compute_structural_shocks(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_hmsh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 1, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# compute structural shocks
shocks         = compute_structural_shocks(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_mix$new(p = 1, M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 1, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# compute structural shocks
shocks         = compute_structural_shocks(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_msh$new(p = 1, M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# compute structural shocks
shocks         = compute_structural_shocks(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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

See Also

estimate, normalise, summary

Examples

specification  = specify_bsvar_t$new(us_fiscal_lsuw, p = 1)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# compute structural shocks
shocks         = compute_structural_shocks(posterior)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_t$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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.

See Also

compute_impulse_responses, estimate, normalise, summary

Examples

specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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.

See Also

compute_impulse_responses, estimate, normalise, summary

Examples

specification  = specify_bsvar$new(us_fiscal_lsuw, p = 1)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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 'PosteriorBSVAREXH'
compute_variance_decompositions(posterior, horizon)

Arguments

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.

See Also

compute_impulse_responses, estimate, normalise, summary

Examples

specification  = specify_bsvar_exh$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_exh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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 'PosteriorBSVARHMSH'
compute_variance_decompositions(posterior, horizon)

Arguments

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.

See Also

compute_impulse_responses, estimate, normalise, summary

Examples

specification  = specify_bsvar_hmsh$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_hmsh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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.

See Also

compute_impulse_responses, estimate, normalise, summary

Examples

specification  = specify_bsvar_mix$new(us_fiscal_lsuw, p = 1, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_mix$new(p = 1, M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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.

See Also

compute_impulse_responses, estimate, normalise, summary

Examples

specification  = specify_bsvar_msh$new(us_fiscal_lsuw, p = 1, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_msh$new(p = 1, M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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 'PosteriorBSVARSV'
compute_variance_decompositions(posterior, horizon)

Arguments

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.

See Also

compute_impulse_responses, estimate, normalise, summary

Examples

specification  = specify_bsvar_sv$new(us_fiscal_lsuw, p = 1)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

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.

See Also

compute_impulse_responses, estimate, normalise, summary

Examples

specification  = specify_bsvar_t$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_t$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

Details

The homoskedastic SVAR model is given by 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.

The structural shocks, U, are temporally and contemporaneously independent and jointly distributed with zero mean and unit variances. The shock density can be either normal or Student-t with shock-specific degrees-of-freedom parameters that are estimated.

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.

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.

See Also

specify_bsvar, specify_bsvar_msh, specify_bsvar_mix, specify_bsvar_sv, normalise

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 (2025). See section Details for the model equations.

Usage

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

Arguments

Details

The homoskedastic SVAR model is given by 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, the structural shocks, U, are temporally and contemporaneously independent and jointly distributed with zero mean and unit variances. The structural shocks can be either normally or Student-t distributed, where in the latter case the shock-specific degrees of freedom parameters are 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:

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.

Lütkepohl, H., Shang, F., Uzeda, L., and Woźniak, T. (2025) Partial identification of structural vector autoregressions with non-centred stochastic volatility. Journal of Econometrics, 1–18, doi:10.1016/j.jeconom.2025.106107.

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.

See Also

specify_bsvar, specify_posterior_bsvar, normalise

Examples

# simple workflow
############################################################
specification  = specify_bsvar$new(us_fiscal_lsuw, p = 4)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar$new(p = 1) |>
  estimate(S = 5) |> 
  estimate(S = 5) -> post

Bayesian estimation of a Structural Vector Autoregression with exogenous heteroskedastic regime changes via Gibbs sampler

Description

Estimates the SVAR with exogenous heteroskedastic regime changes 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 'BSVAREXH'
estimate(specification, S, thin = 1, show_progress = TRUE)

Arguments

Details

The heteroskedastic SVAR model is given by 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, the structural shocks, U, are temporally and contemporaneously independent and jointly distributed with zero mean. The structural shocks can be either normally or Student-t distributed, where in the latter case the shock-specific degrees of freedom parameters are estimated. 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 an exogenous 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 model selection also with this respect is made using function specify_bsvar_exh.

Value

An object of class PosteriorBSVAREXH 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

xi

an MxTxS array with the exogenous regime allocation matrix.

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 BSVAREXH 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.

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. 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

See Also

specify_bsvar_exh, specify_posterior_bsvar_exh, normalise

Examples

# simple workflow
############################################################
spec  = specify_bsvar_exh$new(us_fiscal_lsuw)
burn  = estimate(spec, 5)
post  = estimate(burn, 5)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_exh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) -> post

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

Description

Estimates the SVAR with Heterogeneous Markov-switching heteroskedasticity with M regimes (HMS(M)) proposed by Shang & Woźniak (2025). 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 Shang & Woźniak (2025), Lütkepohl & Woźniak (2020), and Song & Woźniak (2021). See section Details for the model equations.

Usage

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

Arguments

Details

The heteroskedastic SVAR model is given by 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, the structural shocks, U, are temporally and contemporaneously independent and jointly distributed with zero mean. The structural shocks can be either normally or Student-t distributed, where in the latter case the shock-specific degrees of freedom parameters are estimated. The conditional variance of the nth shock at time t is given by:

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

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

Each of the Markov processes s_{n.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.

Value

An object of class PosteriorBSVARHMSH 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 MxMxNxS array with the posterior draws for the transition matrix.

xi

an MxTxNxS array with the posterior draws for the regime allocation matrix.

pi_0

an MxNxS 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 BSVARHMSH 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

Shang, F., and Woźniak, T. (2025) Identification Verification using Structural Vector Autoregressions with Heterogeneous Markov Switching Heteroskedasticity.

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.

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. 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

See Also

specify_bsvar_hmsh, specify_posterior_bsvar_hmsh, normalise

Examples

# simple workflow
############################################################
specification  = specify_bsvar_hmsh$new(us_fiscal_lsuw, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_hmsh$new(M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) -> posterior

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

Details

The heteroskedastic SVAR model is given by 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, the structural shocks, U, are temporally and contemporaneously independent and finite-mixture of normals distributed with zero mean. Alternatively, the structural shocks can be Student-t distributed, where the shock-specific degrees of freedom parameters are estimated. 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.

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. 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

See Also

specify_bsvar_mix, specify_posterior_bsvar_mix, normalise

Examples

# simple workflow
############################################################
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_mix$new(M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) -> post
  

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

Details

The heteroskedastic SVAR model is given by 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, the structural shocks, U, are temporally and contemporaneously independent and jointly distributed with zero mean. The structural shocks can be either normally or Student-t distributed, where in the latter case the shock-specific degrees of freedom parameters are estimated. 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.

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. 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

See Also

specify_bsvar_msh, specify_posterior_bsvar_msh, normalise

Examples

# simple workflow
############################################################
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_msh$new(M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) -> post

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 (2025). 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

Details

The heteroskedastic SVAR model is given by 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, the structural shocks, U, are temporally and contemporaneously independent and jointly distributed with zero mean. The structural shocks can be either normally or Student-t distributed, where in the latter case the shock-specific degrees of freedom parameters are estimated.

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.

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. (2025) Partial identification of structural vector autoregressions with non-centred stochastic volatility. Journal of Econometrics, 1–18, doi:10.1016/j.jeconom.2025.106107.

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.

See Also

specify_bsvar_sv, specify_posterior_bsvar_sv, normalise

Examples

# simple workflow
############################################################
specification  = specify_bsvar_sv$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_sv$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) -> post

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 (2025). See section Details for the model equations.

Usage

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

Arguments

Details

The homoskedastic SVAR model with t-distributed structural shocks is given by 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, the structural shocks, U, are temporally and contemporaneously independent and jointly Student-t distributed with zero mean, unit variances, and estimated equation-specific 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 NxS matrix with the posterior draws for the equation-specific degrees-of-freedom parameter of the Student-t distribution

lambda

an NxTxS array 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.

Lütkepohl, H., Shang, F., Uzeda, L., and Woźniak, T. (2025) Partial identification of structural vector autoregressions with non-centred stochastic volatility. Journal of Econometrics, 1–18, doi:10.1016/j.jeconom.2025.106107.

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.

See Also

specify_bsvar_t, specify_posterior_bsvar_t, normalise

Examples

# simple workflow
############################################################
specification  = specify_bsvar_t$new(us_fiscal_lsuw, p = 4)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_t$new(p = 4) |>
  estimate(S = 5) |> 
  estimate(S = 5) -> 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 (2025). See section Details for the model equations.

Usage

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

Arguments

Details

The homoskedastic SVAR model is given by 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, the structural shocks, U, are temporally and contemporaneously independent and jointly distributed with zero mean and unit variances. The structural shocks can be either normally or Student-t distributed, where in the latter case the shock-specific degrees of freedom parameters are 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:

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.

Lütkepohl, H., Shang, F., Uzeda, L., and Woźniak, T. (2025) Partial identification of structural vector autoregressions with non-centred stochastic volatility. Journal of Econometrics, 1–18, doi:10.1016/j.jeconom.2025.106107.

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.

See Also

specify_bsvar, specify_posterior_bsvar, normalise

Examples

# simple workflow
############################################################
specification  = specify_bsvar$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

Bayesian estimation of a Structural Vector Autoregression with exogenous heteroskedastic regime changes via Gibbs sampler

Description

Estimates the SVAR with exogenous heteroskedastic regime changes 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 'PosteriorBSVAREXH'
estimate(specification, S, thin = 1, show_progress = TRUE)

Arguments

Details

The heteroskedastic SVAR model is given by 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, the structural shocks, U, are temporally and contemporaneously independent and jointly distributed with zero mean. The structural shocks can be either normally or Student-t distributed, where in the latter case the shock-specific degrees of freedom parameters are estimated. 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 an exogenous 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 model selection also with this respect is made using function specify_bsvar_exh.

Value

An object of class PosteriorBSVAREXH 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

xi

an MxTxS array with the exogenous regime allocation matrix.

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 BSVAREXH 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.

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. 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

See Also

specify_bsvar_exh, specify_posterior_bsvar_exh, normalise

Examples

# simple workflow
############################################################
spec  = specify_bsvar_exh$new(us_fiscal_lsuw)
burn  = estimate(spec, 5)
post  = estimate(burn, 5)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_exh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5)  -> post

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

Description

Estimates the SVAR with Heterogeneous Markov-switching heteroskedasticity with M regimes (HMS(M)) proposed by Shang & Woźniak (2025). 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 Shang & Woźniak (2025), Lütkepohl & Woźniak (2020), and Song & Woźniak (2021). See section Details for the model equations.

Usage

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

Arguments

Details

The heteroskedastic SVAR model is given by 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, the structural shocks, U, are temporally and contemporaneously independent and jointly distributed with zero mean. The structural shocks can be either normally or Student-t distributed, where in the latter case the shock-specific degrees of freedom parameters are estimated. The conditional variance of the nth shock at time t is given by:

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

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

Each of the Markov processes s_{n.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.

Value

An object of class PosteriorBSVARHMSH 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 MxMxNxS array with the posterior draws for the transition matrix.

xi

an MxTxNxS array with the posterior draws for the regime allocation matrix.

pi_0

an MxNxS 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 BSVARHMSH 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

Shang, F., and Woźniak, T. (2025) Identification Verification using Structural Vector Autoregressions with Heterogeneous Markov Switching Heteroskedasticity.

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.

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. 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

See Also

specify_bsvar_hmsh, specify_posterior_bsvar_hmsh, normalise

Examples

# simple workflow
############################################################
specification  = specify_bsvar_hmsh$new(us_fiscal_lsuw, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_hmsh$new(M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) -> posterior

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

Arguments

Details

The heteroskedastic SVAR model is given by 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, the structural shocks, U, are temporally and contemporaneously independent and finite-mixture of normals distributed with zero mean. Alternatively, the structural shocks can be Student-t distributed, where the shock-specific degrees of freedom parameters are estimated. 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.

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. 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

See Also

specify_bsvar_mix, specify_posterior_bsvar_mix, normalise

Examples

# simple workflow
############################################################
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_mix$new(M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) -> post
  

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

Arguments

Details

The heteroskedastic SVAR model is given by 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, the structural shocks, U, are temporally and contemporaneously independent and jointly distributed with zero mean. The structural shocks can be either normally or Student-t distributed, where in the latter case the shock-specific degrees of freedom parameters are estimated. 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.

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. 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

See Also

specify_bsvar_msh, specify_posterior_bsvar_msh, normalise

Examples

# simple workflow
############################################################
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_msh$new(M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) -> post

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 (2025). 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 'PosteriorBSVARSV'
estimate(specification, S, thin = 1, show_progress = TRUE)

Arguments

Details

The heteroskedastic SVAR model is given by 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, the structural shocks, U, are temporally and contemporaneously independent and jointly distributed with zero mean. The structural shocks can be either normally or Student-t distributed, where in the latter case the shock-specific degrees of freedom parameters are estimated.

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.

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. (2025) Partial identification of structural vector autoregressions with non-centred stochastic volatility. Journal of Econometrics, 1–18, doi:10.1016/j.jeconom.2025.106107.

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.

See Also

specify_bsvar_sv, specify_posterior_bsvar_sv, normalise

Examples

# simple workflow
############################################################
specification  = specify_bsvar_sv$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_sv$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) -> post

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 (2025). See section Details for the model equations.

Usage

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

Arguments

Details

The homoskedastic SVAR model with t-distributed structural shocks is given by 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, the structural shocks, U, are temporally and contemporaneously independent and jointly Student-t distributed with zero mean, unit variances, and estimated equation-specific 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 NxS matrix with the posterior draws for the equation-specific degrees-of-freedom parameter of the Student-t distribution

lambda

an NxTxS array 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.

Lütkepohl, H., Shang, F., Uzeda, L., and Woźniak, T. (2025) Partial identification of structural vector autoregressions with non-centred stochastic volatility. Journal of Econometrics, 1–18, doi:10.1016/j.jeconom.2025.106107.

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.

See Also

specify_bsvar_t, specify_posterior_bsvar_t, normalise

Examples

# simple workflow
############################################################
specification  = specify_bsvar_t$new(us_fiscal_lsuw, p = 4)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_t$new(p = 4) |>
  estimate(S = 5) |> 
  estimate(S = 5) -> posterior

Forecasting using Bayesian Structural Vector Autoregression

Description

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

Usage

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

Arguments

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

Y

an NxT matrix with the data on dependent variables

forecast_mean

an NxTxS array with the mean of the predictive density

forecast_covariance

an NxTxS array with the covariance of the predictive density

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

specification  = specify_bsvar$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)
predictive     = forecast(posterior, 4)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  forecast(horizon = 4) -> predictive

# conditional forecasting using a model with exogenous variables
############################################################
specification  = specify_bsvar$new(us_fiscal_lsuw, exogenous = us_fiscal_ex)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# 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 |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar$new( exogenous = us_fiscal_ex) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  forecast(
    horizon = 8,
    exogenous_forecast = us_fiscal_ex_forecasts,
    conditional_forecast = us_fiscal_cond_forecasts
  ) |> plot()

Forecasting using Bayesian Structural Vector Autoregression

Description

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

Usage

## S3 method for class 'PosteriorBSVAREXH'
forecast(
  object,
  horizon = 1,
  exogenous_forecast = NULL,
  conditional_forecast = NULL,
  ...
)

Arguments

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

Y

an NxT matrix with the data on dependent variables

forecast_mean

an NxTxS array with the mean of the predictive density

forecast_covariance

an NxTxS array with the covariance of the predictive density

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

specification  = specify_bsvar_exh$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)
predictive     = forecast(posterior, 4)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_exh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  forecast(horizon = 4) -> predictive
  
# conditional forecasting using a model with exogenous variables
############################################################
specification  = specify_bsvar_exh$new(us_fiscal_lsuw, exogenous = us_fiscal_ex)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# 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 |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_exh$new(exogenous = us_fiscal_ex) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  forecast(
    horizon = 8,
    exogenous_forecast = us_fiscal_ex_forecasts,
    conditional_forecast = us_fiscal_cond_forecasts
  ) |> plot()
  

Forecasting using Bayesian Structural Vector Autoregression

Description

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

Usage

## S3 method for class 'PosteriorBSVARHMSH'
forecast(
  object,
  horizon = 1,
  exogenous_forecast = NULL,
  conditional_forecast = NULL,
  ...
)

Arguments

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

Y

an NxT matrix with the data on dependent variables

forecast_mean

an NxTxS array with the mean of the predictive density

forecast_covariance

an NxTxS array with the covariance of the predictive density

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

specification  = specify_bsvar_hmsh$new(us_fiscal_lsuw, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)
predictive     = forecast(posterior, 4)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_hmsh$new(M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  forecast(horizon = 4) -> predictive
  
# forecasting using a model with exogenous variables
############################################################
specification  = specify_bsvar_hmsh$new(us_fiscal_lsuw, M = 2, exogenous = us_fiscal_ex)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_hmsh$new(M = 2, exogenous = us_fiscal_ex) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  forecast(
    horizon = 8,
    exogenous_forecast = us_fiscal_ex_forecasts
  ) |> plot()
  

Forecasting using Bayesian Structural Vector Autoregression

Description

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

Usage

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

Arguments

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

Y

an NxT matrix with the data on dependent variables

forecast_mean

an NxTxS array with the mean of the predictive density

forecast_covariance

an NxTxS array with the covariance of the predictive density

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

specification  = specify_bsvar_mix$new(us_fiscal_lsuw, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)
predictive     = forecast(posterior, 4)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_mix$new(M = 2) |>
  estimate(S = 5) |>
  estimate(S = 5) |>  
  forecast(horizon = 4) -> predictive
  
# conditional forecasting using a model with exogenous variables
############################################################
specification  = specify_bsvar_mix$new(us_fiscal_lsuw, M = 2, exogenous = us_fiscal_ex)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# 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 |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_mix$new(M = 2, exogenous = us_fiscal_ex) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  forecast(
    horizon = 8,
    exogenous_forecast = us_fiscal_ex_forecasts,
    conditional_forecast = us_fiscal_cond_forecasts
  ) |> plot()
 

Forecasting using Bayesian Structural Vector Autoregression

Description

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

Usage

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

Arguments

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

Y

an NxT matrix with the data on dependent variables

forecast_mean

an NxTxS array with the mean of the predictive density

forecast_covariance

an NxTxS array with the covariance of the predictive density

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

specification  = specify_bsvar_msh$new(us_fiscal_lsuw, M = 2)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)
predictive     = forecast(posterior, 4)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_msh$new(M = 2) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  forecast(horizon = 4) -> predictive
  
# conditional forecasting using a model with exogenous variables
############################################################
specification  = specify_bsvar_msh$new(us_fiscal_lsuw, M = 2, exogenous = us_fiscal_ex)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# 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 |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_msh$new(M = 2, exogenous = us_fiscal_ex) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  forecast(
    horizon = 8,
    exogenous_forecast = us_fiscal_ex_forecasts,
    conditional_forecast = us_fiscal_cond_forecasts
  ) |> plot()
  

Forecasting using Bayesian Structural Vector Autoregression

Description

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

Usage

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

Arguments

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

Y

an NxT matrix with the data on dependent variables

forecast_mean

an NxTxS array with the mean of the predictive density

forecast_covariance

an NxTxS array with the covariance of the predictive density

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

specification  = specify_bsvar_sv$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)
predictive     = forecast(posterior, 2)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_sv$new() |>
  estimate(S = 5) |>
  estimate(S = 5) |>  
  forecast(horizon = 2) -> predictive
  
# conditional forecasting using a model with exogenous variables
############################################################
specification  = specify_bsvar_sv$new(us_fiscal_lsuw, exogenous = us_fiscal_ex)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# 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 |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_sv$new(exogenous = us_fiscal_ex) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  forecast(
    horizon = 8,
    exogenous_forecast = us_fiscal_ex_forecasts,
    conditional_forecast = us_fiscal_cond_forecasts
  ) |> plot()

Forecasting using Bayesian Structural Vector Autoregression

Description

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

Usage

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

Arguments

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

Y

an NxT matrix with the data on dependent variables

forecast_mean

an NxTxS array with the mean of the predictive density

forecast_covariance

an NxTxS array with the covariance of the predictive density

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

specification  = specify_bsvar_t$new(us_fiscal_lsuw)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)
predictive     = forecast(posterior, 4)

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_t$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  forecast(horizon = 4) -> predictive

# conditional forecasting using a model with exogenous variables
############################################################
specification  = specify_bsvar_t$new(us_fiscal_lsuw, exogenous = us_fiscal_ex)
burn_in        = estimate(specification, 5)
posterior      = estimate(burn_in, 5)

# 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 |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_t$new(exogenous = us_fiscal_ex) |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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 the structural matrix B

Description

Normalises the sign of rows of matrix B MCMC draws, relative to matrix B_benchmark, provided as the second argument. 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, B_benchmark = NULL)

Arguments

Value

An object of the same class as that provided as the input argument posterior containing the posterior draws including the draws of the normalised structural matrix.

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.

See Also

estimate

Examples

specification  = specify_bsvar$new(us_fiscal_lsuw)        # specify the model
burn_in        = estimate(specification, 5)               # run the burn-in
posterior      = estimate(burn_in, 5)                     # estimate the model

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

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

Description

Normalises the sign of rows of matrix B MCMC draws, relative to matrix B_benchmark, provided as the second argument. 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

## S3 method for class 'PosteriorBSVAR'
normalise(posterior, B_benchmark = NULL)

Arguments

Value

An object of the same class as that provided as the input argument posterior containing the posterior draws including the draws of the normalised structural matrix.

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.

See Also

estimate

Examples

specification  = specify_bsvar$new(us_fiscal_lsuw)        # specify the model
burn_in        = estimate(specification, 5)               # run the burn-in
posterior      = estimate(burn_in, 5)                     # estimate the model

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

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

Description

Normalises the sign of rows of matrix B MCMC draws, relative to matrix B_benchmark, provided as the second argument. 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

## S3 method for class 'PosteriorBSVAREXH'
normalise(posterior, B_benchmark = NULL)

Arguments

Value

An object of the same class as that provided as the input argument posterior containing the posterior draws including the draws of the normalised structural matrix.

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.

See Also

estimate

Examples

specification  = specify_bsvar_exh$new(us_fiscal_lsuw)    # specify the model
burn_in        = estimate(specification, 5)               # run the burn-in
posterior      = estimate(burn_in, 5)                     # estimate the model

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

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

Description

Normalises the sign of rows of matrix B MCMC draws, relative to matrix B_benchmark, provided as the second argument. 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

## S3 method for class 'PosteriorBSVARHMSH'
normalise(posterior, B_benchmark = NULL)

Arguments

Value

An object of the same class as that provided as the input argument posterior containing the posterior draws including the draws of the normalised structural matrix.

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.

See Also

estimate

Examples

specification  = specify_bsvar_hmsh$new(us_fiscal_lsuw)    # specify the model
burn_in        = estimate(specification, 5)               # run the burn-in
posterior      = estimate(burn_in, 5)                     # estimate the model

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

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

Description

Normalises the sign of rows of matrix B MCMC draws, relative to matrix B_benchmark, provided as the second argument. 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

## S3 method for class 'PosteriorBSVARMIX'
normalise(posterior, B_benchmark = NULL)

Arguments

Value

An object of the same class as that provided as the input argument posterior containing the posterior draws including the draws of the normalised structural matrix.

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.

See Also

estimate

Examples

specification  = specify_bsvar_mix$new(us_fiscal_lsuw)    # specify the model
burn_in        = estimate(specification, 5)               # run the burn-in
posterior      = estimate(burn_in, 5)                     # estimate the model

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

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

Description

Normalises the sign of rows of matrix B MCMC draws, relative to matrix B_benchmark, provided as the second argument. 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

## S3 method for class 'PosteriorBSVARMSH'
normalise(posterior, B_benchmark = NULL)

Arguments

Value

An object of the same class as that provided as the input argument posterior containing the posterior draws including the draws of the normalised structural matrix.

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.

See Also

estimate

Examples

specification  = specify_bsvar_msh$new(us_fiscal_lsuw)    # specify the model
burn_in        = estimate(specification, 5)               # run the burn-in
posterior      = estimate(burn_in, 5)                     # estimate the model

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

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

Description

Normalises the sign of rows of matrix B MCMC draws, relative to matrix B_benchmark, provided as the second argument. 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

## S3 method for class 'PosteriorBSVARSV'
normalise(posterior, B_benchmark = NULL)

Arguments

Value

An object of the same class as that provided as the input argument posterior containing the posterior draws including the draws of the normalised structural matrix.

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.

See Also

estimate

Examples

specification  = specify_bsvar_sv$new(us_fiscal_lsuw)     # specify the model
burn_in        = estimate(specification, 5)               # run the burn-in
posterior      = estimate(burn_in, 5)                     # estimate the model

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

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

Description

Normalises the sign of rows of matrix B MCMC draws, relative to matrix B_benchmark, provided as the second argument. 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

## S3 method for class 'PosteriorBSVART'
normalise(posterior, B_benchmark = NULL)

Arguments

Value

An object of the same class as that provided as the input argument posterior containing the posterior draws including the draws of the normalised structural matrix.

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.

See Also

estimate

Examples

specification  = specify_bsvar_t$new(us_fiscal_lsuw)     # specify the model
burn_in        = estimate(specification, 5)               # run the burn-in
posterior      = estimate(burn_in, 5)                     # estimate the model

# normalise the posterior
BB             = posterior$last_draw$starting_values$B    # get the last draw of B
B_benchmark          = diag((-1) * sign(diag(BB))) %*% BB       # set negative diagonal elements
posterior      = normalise(posterior, B_benchmark)              # 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

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

See Also

forecast

Examples

specification  = specify_bsvar$new(us_fiscal_lsuw)    # specify model
burn_in        = estimate(specification, 5)           # run the burn-in
posterior      = estimate(burn_in, 5)                # estimate the model

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

See Also

compute_variance_decompositions

Examples

specification  = specify_bsvar$new(us_fiscal_lsuw)    # specify model
burn_in        = estimate(specification, 5)           # run the burn-in
posterior      = estimate(burn_in, 5)                 # estimate the model

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

See Also

compute_fitted_values

Examples

specification  = specify_bsvar$new(us_fiscal_lsuw)    # specify model
burn_in        = estimate(specification, 5)          # run the burn-in
posterior      = estimate(burn_in, 5)                # estimate the model

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

See Also

compute_historical_decompositions

Examples

specification  = specify_bsvar$new(us_fiscal_lsuw)    # specify model
burn_in        = estimate(specification, 5)           # run the burn-in
posterior      = estimate(burn_in, 5)                 # estimate the model

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

See Also

compute_impulse_responses

Examples

specification  = specify_bsvar$new(us_fiscal_lsuw)   # specify model
burn_in        = estimate(specification, 5)          # run the burn-in
posterior      = estimate(burn_in, 5)                # estimate the model

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

See Also

compute_regime_probabilities

Examples

specification  = specify_bsvar_msh$new(us_fiscal_lsuw)# specify model
burn_in        = estimate(specification, 5)           # run the burn-in
posterior      = estimate(burn_in, 5)                 # estimate the model

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

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar_msh$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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,
  shock_names,
  col = "#ff69b4",
  main,
  xlab,
  mar.multi = c(1, 4.6, 0, 2.1),
  oma.multi = c(6, 0, 5, 0),
  ...
)

Arguments

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

See Also

compute_structural_shocks

Examples

specification  = specify_bsvar$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
shocks         = compute_structural_shocks(posterior)
plot(shocks)                                          # plot

# workflow with the pipe |>
############################################################
us_fiscal_lsuw |>
  specify_bsvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  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

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

See Also

compute_conditional_sd

Examples

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 |>
############################################################
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

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

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,,])

Objects exported from other packages

Description

These objects are imported from other packages. Follow the links below to see their documentation.

generics

forecast()

R6 Class representing the specification of the homoskedastic BSVAR model

Description

The class BSVAR presents complete specification for the homoskedastic bsvar model.

Public fields

Methods

Public methods

• BSVAR$new()

• BSVAR$get_normal()

• BSVAR$get_data_matrices()

• BSVAR$get_identification()

• BSVAR$get_prior()

• BSVAR$get_starting_values()

• BSVAR$clone()

BSVAR$new()

Create a new specification of the homoskedastic bsvar model BSVAR.

Usage

BSVAR$new(
  data,
  p = 1L,
  B,
  A,
  distribution = c("norm", "t"),
  exogenous = NULL,
  stationary = rep(FALSE, ncol(data))
)

Arguments

Returns

A new complete specification for the homoskedastic bsvar model BSVAR.

BSVAR$get_normal()

Returns the logical value of whether the conditional shock distribution is normal.

Usage

BSVAR$get_normal()

Examples

spec = specify_bsvar$new(us_fiscal_lsuw)
spec$get_normal()

BSVAR$get_data_matrices()

Returns the data matrices as the DataMatricesBSVAR object.

Usage

BSVAR$get_data_matrices()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_data_matrices()

BSVAR$get_identification()

Returns the identifying restrictions as the IdentificationBSVARs object.

Usage

BSVAR$get_identification()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_identification()

BSVAR$get_prior()

Returns the prior specification as the PriorBSVAR object.

Usage

BSVAR$get_prior()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_prior()

BSVAR$get_starting_values()

Returns the starting values as the StartingValuesBSVAR object.

Usage

BSVAR$get_starting_values()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_starting_values()

BSVAR$clone()

The objects of this class are cloneable with this method.

Usage

BSVAR$clone(deep = FALSE)

Arguments

See Also

estimate, specify_posterior_bsvar

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar$new(
   data = us_fiscal_lsuw,
   p = 4
)


## ------------------------------------------------
## Method `BSVAR$get_normal()`
## ------------------------------------------------

spec = specify_bsvar$new(us_fiscal_lsuw)
spec$get_normal()


## ------------------------------------------------
## Method `BSVAR$get_data_matrices()`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_data_matrices()


## ------------------------------------------------
## Method `BSVAR$get_identification()`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_identification()


## ------------------------------------------------
## Method `BSVAR$get_prior()`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_prior()


## ------------------------------------------------
## Method `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 BSVAREXH model with exogenous heteroskedastic regime change.

Description

The class BSVAREXH presents complete specification for the BSVAR model with exogenous heteroskedastic regime change.

Public fields

Methods

Public methods

• BSVAREXH$new()

• BSVAREXH$get_normal()

• BSVAREXH$get_data_matrices()

• BSVAREXH$get_identification()

• BSVAREXH$get_prior()

• BSVAREXH$get_starting_values()

• BSVAREXH$clone()

BSVAREXH$new()

Create a new specification of the BSVAR model with Markov Switching Heteroskedasticity, BSVAREXH.

Usage

BSVAREXH$new(
  data,
  p = 1L,
  B,
  A,
  distribution = c("norm", "t"),
  exogenous = NULL,
  stationary = rep(FALSE, ncol(data)),
  variance_regimes = NULL
)

Arguments

Returns

A new complete specification for the bsvar model with exogenous heteroskedastic regime change, BSVAREXH.

BSVAREXH$get_normal()

Returns the logical value of whether the conditional shock distribution is normal.

Usage

BSVAREXH$get_normal()

Examples

spec = specify_bsvar_exh$new(us_fiscal_lsuw)
spec$get_normal()

BSVAREXH$get_data_matrices()

Returns the data matrices as the DataMatricesBSVAR object.

Usage

BSVAREXH$get_data_matrices()

Examples

spec = specify_bsvar_exh$new(us_fiscal_lsuw)
spec$get_data_matrices()

BSVAREXH$get_identification()

Returns the identifying restrictions as the IdentificationBSVARs object.

Usage

BSVAREXH$get_identification()

Examples

spec = specify_bsvar_exh$new(us_fiscal_lsuw)
spec$get_identification()

BSVAREXH$get_prior()

Returns the prior specification as the PriorBSVAREXH object.

Usage

BSVAREXH$get_prior()

Examples

spec = specify_bsvar_exh$new(us_fiscal_lsuw)
spec$get_prior()

BSVAREXH$get_starting_values()

Returns the starting values as the StartingValuesBSVAREXH object.

Usage

BSVAREXH$get_starting_values()

Examples

spec = specify_bsvar_exh$new(us_fiscal_lsuw)
spec$get_starting_values()

BSVAREXH$clone()

The objects of this class are cloneable with this method.

Usage

BSVAREXH$clone(deep = FALSE)

Arguments

See Also

estimate, specify_posterior_bsvar_exh

Examples

spec = specify_bsvar_exh$new(us_fiscal_lsuw)


## ------------------------------------------------
## Method `BSVAREXH$get_normal()`
## ------------------------------------------------

spec = specify_bsvar_exh$new(us_fiscal_lsuw)
spec$get_normal()


## ------------------------------------------------
## Method `BSVAREXH$get_data_matrices()`
## ------------------------------------------------

spec = specify_bsvar_exh$new(us_fiscal_lsuw)
spec$get_data_matrices()


## ------------------------------------------------
## Method `BSVAREXH$get_identification()`
## ------------------------------------------------

spec = specify_bsvar_exh$new(us_fiscal_lsuw)
spec$get_identification()


## ------------------------------------------------
## Method `BSVAREXH$get_prior()`
## ------------------------------------------------

spec = specify_bsvar_exh$new(us_fiscal_lsuw)
spec$get_prior()


## ------------------------------------------------
## Method `BSVAREXH$get_starting_values()`
## ------------------------------------------------

spec = specify_bsvar_exh$new(us_fiscal_lsuw)
spec$get_starting_values()

R6 Class representing the specification of the BSVARHMSH model with Heterogeneous Markov Switching Heteroskedasticity.

Description

The class BSVARHMSH presents complete specification for the BSVAR model with Heterogeneous Markov Switching Heteroskedasticity.

Public fields

Methods

Public methods

• BSVARHMSH$new()

• BSVARHMSH$get_normal()

• BSVARHMSH$get_data_matrices()

• BSVARHMSH$get_identification()

• BSVARHMSH$get_prior()

• BSVARHMSH$get_starting_values()

• BSVARHMSH$clone()

BSVARHMSH$new()

Create a new specification of the BSVAR model with Heterogeneous Markov Switching Heteroskedasticity, BSVARHMSH.

Usage

BSVARHMSH$new(
  data,
  p = 1L,
  M = 2L,
  B,
  A,
  distribution = c("norm", "t"),
  exogenous = NULL,
  stationary = rep(FALSE, ncol(data)),
  finiteM = TRUE
)

Arguments

Returns

A new complete specification for the bsvar model with Heterogeneous Markov Switching Heteroskedasticity, BSVARHMSH.

BSVARHMSH$get_normal()

Returns the logical value of whether the conditional shock distribution is normal.

Usage

BSVARHMSH$get_normal()

Examples

spec = specify_bsvar_hmsh$new(us_fiscal_lsuw)
spec$get_normal()

BSVARHMSH$get_data_matrices()

Returns the data matrices as the DataMatricesBSVAR object.

Usage

BSVARHMSH$get_data_matrices()

Examples

spec = specify_bsvar_hmsh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$get_data_matrices()

BSVARHMSH$get_identification()

Returns the identifying restrictions as the IdentificationBSVARs object.

Usage

BSVARHMSH$get_identification()

Examples

spec = specify_bsvar_hmsh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$get_identification()

BSVARHMSH$get_prior()

Returns the prior specification as the PriorBSVARMSH object.

Usage

BSVARHMSH$get_prior()

Examples

spec = specify_bsvar_hmsh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$get_prior()

BSVARHMSH$get_starting_values()

Returns the starting values as the StartingValuesBSVARHMSH object.

Usage

BSVARHMSH$get_starting_values()

Examples

spec = specify_bsvar_hmsh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$get_starting_values()

BSVARHMSH$clone()

The objects of this class are cloneable with this method.

Usage

BSVARHMSH$clone(deep = FALSE)

Arguments

See Also

estimate, specify_posterior_bsvar_hmsh

Examples

spec = specify_bsvar_hmsh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)


## ------------------------------------------------
## Method `BSVARHMSH$get_normal()`
## ------------------------------------------------

spec = specify_bsvar_hmsh$new(us_fiscal_lsuw)
spec$get_normal()


## ------------------------------------------------
## Method `BSVARHMSH$get_data_matrices()`
## ------------------------------------------------

spec = specify_bsvar_hmsh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$get_data_matrices()


## ------------------------------------------------
## Method `BSVARHMSH$get_identification()`
## ------------------------------------------------

spec = specify_bsvar_hmsh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$get_identification()


## ------------------------------------------------
## Method `BSVARHMSH$get_prior()`
## ------------------------------------------------

spec = specify_bsvar_hmsh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$get_prior()


## ------------------------------------------------
## Method `BSVARHMSH$get_starting_values()`
## ------------------------------------------------

spec = specify_bsvar_hmsh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$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

BSVARMSH -> BSVARMIX

Public fields

Methods

Public methods

• BSVARMIX$new()

• BSVARMIX$clone()

BSVARMIX$new()

Create a new specification of the BSVAR model with a zero-mean mixture of normals model for structural shocks, BSVARMIX.

Usage

BSVARMIX$new(
  data,
  p = 1L,
  M = 2L,
  B,
  A,
  distribution = c("norm", "t"),
  exogenous = NULL,
  stationary = rep(FALSE, ncol(data)),
  finiteM = TRUE
)

Arguments

Returns

A new complete specification for the bsvar model with a zero-mean mixture of normals model for structural shocks, BSVARMIX.

BSVARMIX$clone()

The objects of this class are cloneable with this method.

Usage

BSVARMIX$clone(deep = FALSE)

Arguments

See Also

estimate, specify_posterior_bsvar_mix

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

Methods

Public methods

• BSVARMSH$new()

• BSVARMSH$get_normal()

• BSVARMSH$get_data_matrices()

• BSVARMSH$get_identification()

• BSVARMSH$get_prior()

• BSVARMSH$get_starting_values()

• BSVARMSH$clone()

BSVARMSH$new()

Create a new specification of the BSVAR model with Markov Switching Heteroskedasticity, BSVARMSH.

Usage

BSVARMSH$new(
  data,
  p = 1L,
  M = 2L,
  B,
  A,
  distribution = c("norm", "t"),
  exogenous = NULL,
  stationary = rep(FALSE, ncol(data)),
  finiteM = TRUE
)

Arguments

Returns

A new complete specification for the bsvar model with Markov Switching Heteroskedasticity, BSVARMSH.

BSVARMSH$get_normal()

Returns the logical value of whether the conditional shock distribution is normal.

Usage

BSVARMSH$get_normal()

Examples

spec = specify_bsvar_msh$new(us_fiscal_lsuw)
spec$get_normal()

BSVARMSH$get_data_matrices()

Returns the data matrices as the DataMatricesBSVAR object.

Usage

BSVARMSH$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()

BSVARMSH$get_identification()

Returns the identifying restrictions as the IdentificationBSVARs object.

Usage

BSVARMSH$get_identification()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_msh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$get_identification()

BSVARMSH$get_prior()

Returns the prior specification as the PriorBSVARMSH object.

Usage

BSVARMSH$get_prior()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_msh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$get_prior()

BSVARMSH$get_starting_values()

Returns the starting values as the StartingValuesBSVARMSH object.

Usage

BSVARMSH$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()

BSVARMSH$clone()

The objects of this class are cloneable with this method.

Usage

BSVARMSH$clone(deep = FALSE)

Arguments

See Also

estimate, specify_posterior_bsvar_msh

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_msh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)


## ------------------------------------------------
## Method `BSVARMSH$get_normal()`
## ------------------------------------------------

spec = specify_bsvar_msh$new(us_fiscal_lsuw)
spec$get_normal()


## ------------------------------------------------
## Method `BSVARMSH$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 `BSVARMSH$get_identification()`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar_msh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$get_identification()


## ------------------------------------------------
## Method `BSVARMSH$get_prior()`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar_msh$new(
   data = us_fiscal_lsuw,
   p = 4,
   M = 2
)
spec$get_prior()


## ------------------------------------------------
## Method `BSVARMSH$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

Methods

Public methods

• BSVARSV$new()

• BSVARSV$get_normal()

• BSVARSV$get_data_matrices()

• BSVARSV$get_identification()

• BSVARSV$get_prior()

• BSVARSV$get_starting_values()

• BSVARSV$clone()

BSVARSV$new()

Create a new specification of the BSVAR model with Stochastic Volatility heteroskedasticity, BSVARSV.

Usage

BSVARSV$new(
  data,
  p = 1L,
  B,
  A,
  distribution = c("norm", "t"),
  exogenous = NULL,
  centred_sv = FALSE,
  stationary = rep(FALSE, ncol(data))
)

Arguments

Returns

A new complete specification for the bsvar model with Stochastic Volatility heteroskedasticity, BSVARSV.

BSVARSV$get_normal()

Returns the logical value of whether the conditional shock distribution is normal.

Usage

BSVARSV$get_normal()

Examples

spec = specify_bsvar_sv$new(us_fiscal_lsuw)
spec$get_normal()

BSVARSV$get_data_matrices()

Returns the data matrices as the DataMatricesBSVAR object.

Usage

BSVARSV$get_data_matrices()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_sv$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_data_matrices()

BSVARSV$get_identification()

Returns the identifying restrictions as the IdentificationBSVARs object.

Usage

BSVARSV$get_identification()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_sv$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_identification()

BSVARSV$get_prior()

Returns the prior specification as the PriorBSVARSV object.

Usage

BSVARSV$get_prior()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_sv$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_prior()

BSVARSV$get_starting_values()

Returns the starting values as the StartingValuesBSVARSV object.

Usage

BSVARSV$get_starting_values()

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_sv$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_starting_values()

BSVARSV$clone()

The objects of this class are cloneable with this method.

Usage

BSVARSV$clone(deep = FALSE)

Arguments

See Also

estimate, specify_posterior_bsvar_sv

Examples

data(us_fiscal_lsuw)
spec = specify_bsvar_sv$new(
   data = us_fiscal_lsuw,
   p = 4
)


## ------------------------------------------------
## Method `BSVARSV$get_normal()`
## ------------------------------------------------

spec = specify_bsvar_sv$new(us_fiscal_lsuw)
spec$get_normal()


## ------------------------------------------------
## Method `BSVARSV$get_data_matrices()`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar_sv$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_data_matrices()


## ------------------------------------------------
## Method `BSVARSV$get_identification()`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar_sv$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_identification()


## ------------------------------------------------
## Method `BSVARSV$get_prior()`
## ------------------------------------------------

data(us_fiscal_lsuw)
spec = specify_bsvar_sv$new(
   data = us_fiscal_lsuw,
   p = 4
)
spec$get_prior()


## ------------------------------------------------
## Method `BSVARSV$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

BSVAR -> BSVART

Public fields

Methods

Public methods

• BSVART$new()

• BSVART$clone()

BSVART$new()

Create a new specification of the BSVAR model with t-distributed structural shocks, BSVART.

Usage

BSVART$new(
  data,
  p = 1L,
  B,
  A,
  exogenous = NULL,
  stationary = rep(FALSE, ncol(data))
)

Arguments

Returns

A new complete specification for the bsvar model with t-distributed structural shocks, BSVART.

BSVART$clone()

The objects of this class are cloneable with this method.

Usage

BSVART$clone(deep = FALSE)

Arguments

See Also

estimate, specify_posterior_bsvar_t

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

Methods

Public methods

• DataMatricesBSVAR$new()

• DataMatricesBSVAR$get_data_matrices()

• DataMatricesBSVAR$clone()

DataMatricesBSVAR$new()

Create new data matrices DataMatricesBSVAR.

Usage

DataMatricesBSVAR$new(data, p = 1L, exogenous = NULL)

Arguments

Returns

New data matrices DataMatricesBSVAR.

DataMatricesBSVAR$get_data_matrices()

Returns the data matrices DataMatricesBSVAR as a list.

Usage

DataMatricesBSVAR$get_data_matrices()

Examples

data(us_fiscal_lsuw)
YX = specify_data_matrices$new(data = us_fiscal_lsuw, p = 4)
YX$get_data_matrices()

DataMatricesBSVAR$clone()

The objects of this class are cloneable with this method.

Usage

DataMatricesBSVAR$clone(deep = FALSE)

Arguments

Examples

data(us_fiscal_lsuw)
YX = specify_data_matrices$new(data = us_fiscal_lsuw, p = 4)
dim(YX$Y); dim(YX$X)


## ------------------------------------------------
## Method `DataMatricesBSVAR$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 Forecasts

Description

R6 class representing draws from the predictive density of a Bayesian Structural Vector Autoregression model.

Details

The class contains the following objects:

forecasts

An N x horizon x S array containing draws from the predictive density.

forecast_mean

An N x horizon x S array containing the conditional means of the predictive density.

forecast_covariance

An N x N x horizon x S array containing the conditional covariance matrices of the predictive density.

Y

An N x T matrix containing the data on the dependent variables used for estimation.

The method as_list() returns the contents of the Forecasts object as a list.

Value

An object of class Forecasts.

Public fields

Methods

Public methods

• Forecasts$new()

• Forecasts$get_forecasts()

• Forecasts$clone()

Forecasts$new()

Creates a new Forecasts object from the output of the forecasting procedure.

Usage

Forecasts$new(output, Y)

Arguments

Returns

An object of class Forecasts.

Forecasts$get_forecasts()

Converts the Forecasts object to a list.

Usage

Forecasts$get_forecasts()

Returns

A list containing forecasts, forecast_mean, forecast_covariance, and Y.

Forecasts$clone()

The objects of this class are cloneable with this method.

Usage

Forecasts$clone(deep = FALSE)

Arguments

Examples

spec = specify_bsvar$new(us_fiscal_lsuw)
burn = estimate(spec, 5)
post = estimate(burn, 5)
fore = forecast(post, 4)
apply(fore$forecasts, 1:2, mean) # compute mean forecasts 

R6 Class Representing IdentificationBSVARs

Description

The class IdentificationBSVARs presents the identifying restrictions for the bsvar models.

Public fields

Methods

Public methods

• IdentificationBSVARs$new()

• IdentificationBSVARs$get_identification()

• IdentificationBSVARs$set_identification()

• IdentificationBSVARs$clone()

IdentificationBSVARs$new()

Create new identifying restrictions IdentificationBSVARs.

Usage

IdentificationBSVARs$new(B, A, N, K)

Arguments

Returns

Identifying restrictions IdentificationBSVARs.

IdentificationBSVARs$get_identification()

Returns the elements of the identification pattern IdentificationBSVARs as a list.

Usage

IdentificationBSVARs$get_identification()

Examples

B    = matrix(c(TRUE,TRUE,TRUE,FALSE,FALSE,TRUE,FALSE,TRUE,TRUE), 3, 3); B
spec = specify_identification_bsvars$new(B = B, N = 3, K = 4)
spec$get_identification()

IdentificationBSVARs$set_identification()

Set new starting values StartingValuesBSVAR.

Usage

IdentificationBSVARs$set_identification(B, A, N, K)

Arguments

Examples

spec = specify_identification_bsvars$new(N = 3, K = 4) # specify a model with the default option
B    = matrix(c(TRUE,TRUE,TRUE,FALSE,FALSE,TRUE,FALSE,TRUE,TRUE), 3, 3); B
spec$set_identification(B = B, N = 3, K = 4)  # modify an existing specification
spec$get_identification()              # check the outcome

IdentificationBSVARs$clone()

The objects of this class are cloneable with this method.

Usage

IdentificationBSVARs$clone(deep = FALSE)

Arguments

Examples

specify_identification_bsvars$new(N = 3, K = 4) # 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(B = B, N = 3, K = 4) # an alternative identification pattern


## ------------------------------------------------
## Method `IdentificationBSVARs$get_identification()`
## ------------------------------------------------

B    = matrix(c(TRUE,TRUE,TRUE,FALSE,FALSE,TRUE,FALSE,TRUE,TRUE), 3, 3); B
spec = specify_identification_bsvars$new(B = B, N = 3, K = 4)
spec$get_identification()


## ------------------------------------------------
## Method `IdentificationBSVARs$set_identification()`
## ------------------------------------------------

spec = specify_identification_bsvars$new(N = 3, K = 4) # specify a model with the default option
B    = matrix(c(TRUE,TRUE,TRUE,FALSE,FALSE,TRUE,FALSE,TRUE,TRUE), 3, 3); B
spec$set_identification(B = B, N = 3, K = 4)  # modify an existing specification
spec$get_identification()              # check the outcome