Package {bvars}

Type: Package
Title: Bayesian Forecasting with Large Vector Autoregressions
Version: 1.0
Date: 2026-06-03
Maintainer: Tomasz Woźniak <wozniak.tom@pm.me>
Description: Provides fast and efficient procedures for Bayesian estimation and forecasting using state-of-the-art Vector Autoregressions. This package includes the model proposed by Chan (2020) <doi:10.1080/07350015.2018.1451336>, that is, a Bayesian Vector Autoregression with Minnesota priors and a flexible structure of the error term specification. The latter includes: conditional multivariate normal or Student’s t distributions, as well as homoskedastic or heteroskedastic specifications with a common volatility modelled by centred or non-centred Stochastic Volatility. Additionally, the package facilitates predictive analyses using density forecasting and forecast-error variance decompositions. All this is complemented by simple workflows, useful plots and summary functions, and comprehensive documentation. The 'bvars' package aligns with R packages 'bsvars' by Woźniak (2024) <doi:10.32614/CRAN.package.bsvars>, 'bsvarSIGNs' by Wang & Woźniak (2025) <doi:10.32614/CRAN.package.bsvarSIGNs>, and 'bpvars' by Woźniak (2025) <doi:10.32614/CRAN.package.bpvars> regarding objects, workflows, and code structure, and they constitute an integrated toolset.
License: GPL (≥ 3)
Depends: R (≥ 4.1.0), RcppArmadillo, bsvars
Imports: generics, Rcpp (≥ 1.0.14), RcppProgress, RcppTN, R6
LinkingTo: Rcpp, RcppArmadillo, RcppProgress, RcppTN, bsvars
URL: https://bsvars.org/bvars/
BugReports: https://github.com/bsvars/bvars/issues
Encoding: UTF-8
LazyData: true
RoxygenNote: 7.3.3
NeedsCompilation: yes
Packaged: 2026-06-03 08:54:49 UTC; twozniak
Author: Rui Liu ORCID iD [aut], Andrés Ramirez Hassan ORCID iD [aut], Tomasz Woźniak ORCID iD [aut, cre, cph]
Repository: CRAN
Date/Publication: 2026-06-08 19:40:12 UTC

Bayesian Forecasting with Large Vector Autoregressions

Description

Provides fast and efficient procedures for Bayesian estimation and forecasting using state-of-the-art Vector Autoregressions. This package includes the model proposed by Chan (2020) <doi:10.1080/07350015.2018.1451336>, that is, a Bayesian Vector Autoregression with Minnesota priors and a flexible structure of the error term specification. The latter includes: conditional multivariate normal or Student’s t distributions, as well as homoskedastic or heteroskedastic specifications with a common volatility modelled by centred or non-centred Stochastic Volatility. Additionally, the package facilitates predictive analyses using density forecasting and forecast-error variance decompositions. All this is complemented by simple workflows, useful plots and summary functions, and comprehensive documentation. The 'bvars' package aligns with R packages 'bsvars' by Woźniak (2024) <doi:10.32614/CRAN.package.bsvars>, 'bsvarSIGNs' by Wang & Woźniak (2025) <doi:10.32614/CRAN.package.bsvarSIGNs>, and 'bpvars' by Woźniak (2025) <doi:10.32614/CRAN.package.bpvars> regarding objects, workflows, and code structure, and they constitute an integrated toolset.

Details

Models. All the BVAR 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.

This package assumes that the error matrix follows a matrix normal distribution:

E \mid X \sim \mathcal{MN}_{N \times T}(\mathbf{0}, \mathbf{\Sigma}, \mathbf{\Omega})

where \Sigma is the NxN covariance matrix of the error term at time t, and \Omega is a TxT diagonal matrix.

The diagonal elements of \Omega determine the specification of the error term covariance structure. Specifically, the error term at time t follows the multivariate normal distribution

e_t \sim \mathcal{N}_N(\mathbf{0}, \sigma_t^2\lambda_t \mathbf{\Sigma})

where the scalar processes \sigma_t^2 and \lambda_t determine the diagonal elements of \Omega. The process \sigma_t^2 specifies conditional variance and includes three options:

\sigma_t^2 = 1

homoskedastic error term

\sigma_t^2

estimated and following non-centred stochastic volatility

\sigma_t^2

estimated and following centred stochastic volatility

The process \lambda_t specifies the conditional distribution of the error term and includes two options:

\lambda_t = 1

Gaussian error term specification

\lambda_t

estimated and following a priori an inverse gamma 2 distribution \mathcal{IG}2(\nu - 2, \nu), where \nu > 2 is a degrees of freedom parameter

Prior distributions. The autoregressive matrix A is assigned matrix-variate normal distribution:

\mathbf{A} \mid \underline{\mathbf{A}}, \mathbf{V}, \boldsymbol{\Sigma} \sim \mathcal{MN}_{N \times K}(\underline{\mathbf{A}}, \boldsymbol{\Sigma}, \mathbf{V})

with the mean matrix \underline{\mathbf{A}}, and covariance matrices \boldsymbol{\Sigma}_{N\times N} and \mathbf{V}_{K\times K} defining the row- and column-covariance structures.

This is complemented by the inverse Wishart prior for the error term covariance \boldsymbol{\Sigma}:

\boldsymbol{\Sigma} \mid \underline{\mathbf{S}}, \underline{\nu} \sim \mathcal{IW}(\underline{\mathbf{S}}, \underline{\nu})

with the scale matrix \underline{\mathbf{S}} and degrees of freedom \underline{\nu}.

Note

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

Author(s)

Rui Liu rl3023@columbia.edu, Andres Ramirez Hassan aramir21@gmail.com, Tomasz Woźniak wozniak.tom@pm.me

References

Chan (2020) Large Bayesian VARs: A Flexible Kronecker Error Covariance Structure, Journal of Business and Economic Statistics, 38(1), 68–79, <doi:10.1080/07350015.2018.1451336>.

See Also

Useful links:

Examples

# simple workflow
############################################################
spec = specify_bvar$new(us_macro_chan)        # specify the model
burn = estimate(spec, 5)                      # run the burn-in
post = estimate(burn, 10)                     # estimate the model

# workflow with the pipe |>
############################################################
us_macro_chan |>
  specify_bvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 10) -> post

Computes posterior draws from data predictive density

Description

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

Usage

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

Arguments

posterior

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

Value

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

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

spec = specify_bvar$new(us_macro_chan)        # specify the model
burn = estimate(spec, 5)                      # run the burn-in
post = estimate(burn, 10)                     # estimate the model
fitt = compute_fitted_values(post)            # fitted values

# workflow with the pipe |>
############################################################
us_macro_chan |>
  specify_bvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  compute_fitted_values() -> fitt

Computes posterior draws of shocks

Description

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

Usage

compute_shocks(posterior)

Arguments

posterior

posterior estimation outcome obtained by running the estimate function.

Value

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

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# simple workflow
############################################################
spec = specify_bvar$new(us_macro_chan)        # specify the model
burn = estimate(spec, 5)                      # run the burn-in
post = estimate(burn, 10)                     # estimate the model
shoc = compute_shocks(post)                   # compute shocks
plot(shoc)

# workflow with the pipe |>
############################################################
us_macro_chan |>
  specify_bvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 10) |> 
  compute_shocks() |> plot()

Computes posterior draws of shocks

Description

Each of the draws from the posterior estimation of the BAVR model is transformed into a draw from the posterior distribution of the shocks.

Usage

## S3 method for class 'PosteriorBVAR'
compute_shocks(posterior)

Arguments

posterior

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

Value

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

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# simple workflow
############################################################
spec = specify_bvar$new(us_macro_chan)        # specify the model
burn = estimate(spec, 5)                      # run the burn-in
post = estimate(burn, 10)                     # estimate the model
shoc = compute_shocks(post)                   # compute shocks

# workflow with the pipe |>
############################################################
us_macro_chan |>
  specify_bvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 10) |> 
  compute_shocks() -> shoc

Computes posterior draws of the forecast error variance decomposition

Description

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

Usage

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

Arguments

posterior

posterior estimation outcome obtained by running the estimate function.

horizon

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

Value

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

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

References

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

Examples

spec = specify_bvar$new(us_macro_chan)        # specify the model
burn = estimate(spec, 5)                      # run the burn-in
post = estimate(burn, 10)                     # estimate the model
fevd = compute_variance_decompositions(post, horizon = 4)

# workflow with the pipe |>
############################################################
us_macro_chan |>
  specify_bvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 10) |> 
  compute_variance_decompositions(horizon = 4) -> fevd

Bayesian Estimation via Gibbs sampler of a Bayesian VAR with a Flexible Error Term Specification

Description

Estimates the model by Chan (2020) <doi:10.1080/07350015.2018.1451336>, that is, a Bayesian Vector Autoregression with Minnesota priors and a flexible structure of the error term specification. The latter includes: conditional multivariate normal or Student’s t distributions, as well as homoskedastic or heteroskedastic specifications with a common volatility modelled by centred or non-centred Stochastic Volatility. The estimation is conducted via an efficient Gibbs sampler employing frontier numerical techniques and algorithms written in C++ for excellent computational speed.

Usage

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

Arguments

specification

an object of class BVAR generated using the specify_bvar$new() function.

S

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

thin

a positive integer, specifying the frequency of MCMC output thinning

show_progress

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

Value

An object of class PosteriorBVAR 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

Sigma

an NxNxS array with the posterior draws for matrix \Sigma

V

a KxKxS array with the posterior draws for the hyper-parameter matrix \Sigma

last_draw an object of class BVAR 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)

Rui Liu rl3023@columbia.edu, Andres Ramirez Hassan aramir21@gmail.com & Tomasz Woźniak wozniak.tom@pm.me

References

Barndorff-Nielsen, Blaesild, Jensen, Jorgensen (1982) Exponential Transformation Models, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 379, 41–-65, <doi:10.1098/rspa.1982.0004>.

Chan (2020) Large Bayesian VARs: A Flexible Kronecker Error Covariance Structure, Journal of Business and Economic Statistics, 38(1), 68–79, <doi:10.1080/07350015.2018.1451336>.

Hamura, Irie, Sugasawa (2024) Gibbs Sampler for Matrix Generalized Inverse Gaussian Distributions, Journal of Computational and Graphical Statistics, 33(2), 331–340, <doi:10.1080/10618600.2023.2258186>.

Thabane, Safiul Haq (2004) On the Matrix-Variate Generalized Hyperbolic Distribution and Its Bayesian Applications, Statistics: A Journal of Theoretical and Applied Statistics, 38(6), 511–526, <doi:10.1080/02331880412331319279>.

Woźniak (2016) Bayesian Vector Autoregressions, Australian Economic Review, 49(3), 365–380, <doi:10.1111/1467-8462.12179>.

See Also

specify_bvar, specify_posterior_bvar

Examples

# simple workflow
############################################################
spec = specify_bvar$new(us_macro_chan)        # specify the model
burn = estimate(spec, 5)                      # run the burn-in
post = estimate(burn, 10)                     # estimate the model

# workflow with the pipe |>
############################################################
us_macro_chan |>
  specify_bvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 10) -> post

Bayesian Estimation via Gibbs sampler of a Bayesian VAR with a Flexible Error Term Specification

Description

Estimates the model by Chan (2020) <doi:10.1080/07350015.2018.1451336>, that is, a Bayesian Vector Autoregression with Minnesota priors and a flexible structure of the error term specification. The latter includes: conditional multivariate normal or Student’s t distributions, as well as homoskedastic or heteroskedastic specifications with a common volatility modelled by centred or non-centred Stochastic Volatility. The estimation is conducted via an efficient Gibbs sampler employing frontier numerical techniques and algorithms written in C++ for excellent computational speed.

Usage

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

Arguments

specification

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

S

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

thin

a positive integer, specifying the frequency of MCMC output thinning

show_progress

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

Value

An object of class PosteriorBVAR 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

Sigma

an NxNxS array with the posterior draws for matrix \Sigma

V

a KxKxS array with the posterior draws for the hyper-parameter matrix \Sigma

last_draw an object of class BVAR 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)

Rui Liu rl3023@columbia.edu, Andres Ramirez Hassan aramir21@gmail.com & Tomasz Woźniak wozniak.tom@pm.me

References

Barndorff-Nielsen, Blaesild, Jensen, Jorgensen (1982) Exponential Transformation Models, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 379, 41–-65, <doi:10.1098/rspa.1982.0004>.

Chan (2020) Large Bayesian VARs: A Flexible Kronecker Error Covariance Structure, Journal of Business and Economic Statistics, 38(1), 68–79, <doi:10.1080/07350015.2018.1451336>.

Hamura, Irie, Sugasawa (2024) Gibbs Sampler for Matrix Generalized Inverse Gaussian Distributions, Journal of Computational and Graphical Statistics, 33(2), 331–340, <doi:10.1080/10618600.2023.2258186>.

Thabane, Safiul Haq (2004) On the Matrix-Variate Generalized Hyperbolic Distribution and Its Bayesian Applications, Statistics: A Journal of Theoretical and Applied Statistics, 38(6), 511–526, <doi:10.1080/02331880412331319279>.

Woźniak (2016) Bayesian Vector Autoregressions, Australian Economic Review, 49(3), 365–380, <doi:10.1111/1467-8462.12179>.

See Also

specify_bvar, specify_posterior_bvar

Examples

# simple workflow
############################################################
spec = specify_bvar$new(us_macro_chan)        # specify the model
burn = estimate(spec, 5)                      # run the burn-in
post = estimate(burn, 10)                     # estimate the model

# workflow with the pipe |>
############################################################
us_macro_chan |>
  specify_bvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 10) -> post

Forecasting using Structural Vector Autoregression

Description

Samples from the joint predictive density of all of the dependent variables for the model by Chan (2020) <doi:10.1080/07350015.2018.1451336>, that is, a Bayesian Vector Autoregression with Minnesota priors and a flexible structure of the error term specification. The latter includes: conditional multivariate normal or Student’s t distributions, as well as homoskedastic or heteroskedastic specifications with a common volatility modelled by centred or non-centred Stochastic Volatility.

Usage

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

Arguments

object

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

horizon

a positive integer, specifying the forecasting horizon.

exogenous_forecast

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

conditional_forecast

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

...

not used

Value

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

forecasts

an NxTxS array with the draws from predictive density

forecast_mean

an NxhorizonxS array with the mean of the predictive density

forecast_covariance

an NxNxhorizonxS array with the covariance of the predictive density

Y

an NxT matrix with the data on dependent variables

Author(s)

Rui Liu rl3023@columbia.edu, Andres Ramirez Hassan aramir21@gmail.com & Tomasz Woźniak wozniak.tom@pm.me

Examples

spec = specify_bvar$new(us_macro_chan)   # specify the model
burn = estimate(spec, 5)                      # run the burn-in
post = estimate(burn, 5)                     # estimate the model
pred = forecast(post, 4)                      # forecast 1 year ahead

# workflow with the pipe |>
############################################################
set.seed(123)
us_macro_chan |>
  specify_bvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 5) |> 
  forecast(horizon = 4) -> pred

Objects exported from other packages

Description

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

generics

forecast

Samples random numbers from the matrix-variate normal distribution

Description

Samples random numbers from the matrix-variate normal distribution

Usage

rmatnorm1(M, V, S)

Arguments

M

a real-valued matrix of the expected values

V

a positive definite symmetric matrix of column-specific covariance

S

a positive definite symmetric matrix of row-specific covariance

Value

a matrix - a draw from the matrix-variate normal distribution

Examples

rmatnorm1(matrix(0, 2, 3), diag(2), diag(3))

R6 Class representing the specification of the BVAR model

Description

The class BVAR presents complete specification for the BVAR model.

Public fields

p

a non-negative integer specifying the autoregressive lag order of the model.

prior

an object PriorBVAR with the prior specification.

data_matrices

an object DataMatricesBSVAR with the data matrices.

starting_values

an object StartingValuesBVAR with the starting values.

Methods

Public methods

Method new()

Create a new specification of the BVAR model.

Usage
specify_bvar$new(
  data,
  p = 1L,
  exogenous = NULL,
  common_volatility = c("homoskedastic", "ncSV", "cSV"),
  distribution = c("norm", "t"),
  stationary = rep(FALSE, ncol(data))
)
Arguments
data

a (T+p)xN matrix with time series data.

p

a positive integer providing model's autoregressive lag order.

exogenous

a (T+p)xd matrix of exogenous variables.

common_volatility

a character string specifying the common volatility component of the error term covariance matrix. It can take three values: homoskedastic - the model assumes homoskedastic errors, ncSV - the model assumes non-centred stochastic volatility, and cSV - the model assumes centred stochastic volatility.

distribution

a character string specifying the conditional distribution of structural shocks. Value "norm" sets it to the normal distribution, while value "t" sets the Student-t distribution.

stationary

an N logical vector - its element set to FALSE sets the prior mean for the autoregressive parameters of the Nth equation to the white noise process, otherwise to random walk.

Returns

A new complete specification for the BVAR model.

Method get_normal()

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

Usage
specify_bvar$get_normal()
Examples
spec = specify_bvar$new(us_macro_chan)
spec$get_normal()

Method get_homoskedastic()

Returns the logical value of whether the common volatility is homoskedastic.

Usage
specify_bvar$get_homoskedastic()
Examples
spec = specify_bvar$new(us_macro_chan)
spec$get_homoskedastic()

Method get_centred_sv()

Returns the logical value of whether the common volatility is centred Stochastic Volatility

Usage
specify_bvar$get_centred_sv()
Examples
spec = specify_bvar$new(us_macro_chan)
spec$get_centred_sv()

Method get_data_matrices()

Returns the data matrices as the DataMatricesBSVAR object.

Usage
specify_bvar$get_data_matrices()
Examples
spec = specify_bvar$new(us_macro_chan)
spec$get_data_matrices()

Method get_prior()

Returns the prior specification as the PriorBVAR object.

Usage
specify_bvar$get_prior()
Examples
spec = specify_bvar$new(us_macro_chan)
spec$get_prior()

Method get_starting_values()

Returns the starting values as the StartingValuesBVAR object.

Usage
specify_bvar$get_starting_values()
Examples
spec = specify_bvar$new(us_macro_chan)
spec$get_starting_values()

Method clone()

The objects of this class are cloneable with this method.

Usage
specify_bvar$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Examples

spec = specify_bvar$new(us_macro_chan)


## ------------------------------------------------
## Method `specify_bvar$get_normal`
## ------------------------------------------------

spec = specify_bvar$new(us_macro_chan)
spec$get_normal()


## ------------------------------------------------
## Method `specify_bvar$get_homoskedastic`
## ------------------------------------------------

spec = specify_bvar$new(us_macro_chan)
spec$get_homoskedastic()


## ------------------------------------------------
## Method `specify_bvar$get_centred_sv`
## ------------------------------------------------

spec = specify_bvar$new(us_macro_chan)
spec$get_centred_sv()


## ------------------------------------------------
## Method `specify_bvar$get_data_matrices`
## ------------------------------------------------

spec = specify_bvar$new(us_macro_chan)
spec$get_data_matrices()


## ------------------------------------------------
## Method `specify_bvar$get_prior`
## ------------------------------------------------

spec = specify_bvar$new(us_macro_chan)
spec$get_prior()


## ------------------------------------------------
## Method `specify_bvar$get_starting_values`
## ------------------------------------------------

spec = specify_bvar$new(us_macro_chan)
spec$get_starting_values()

R6 Class Representing PosteriorBVAR

Description

The class PosteriorBVAR contains posterior output and the specification including the last MCMC draw for the BVAR model. Note that due to the thinning of the MCMC output the starting value in element last_draw might not be equal to the last draw provided in element posterior.

Public fields

last_draw

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

posterior

a list containing Bayesian estimation output collected in elements A, Sigma, and V.

Methods

Public methods

Method new()

Create a new posterior output PosteriorBVAR.

Usage
specify_posterior_bvar$new(specification_bvar, posterior_bvar)
Arguments
specification_bvar

an object of class BVAR with the last draw of the current MCMC run as the starting value.

posterior_bvar

a list containing Bayesian estimation output collected in elements A, Sigma, and V.

Returns

A posterior output PosteriorBVAR.

Method get_posterior()

Returns a list containing Bayesian estimation output collected in elements A, Sigma, and V.

Usage
specify_posterior_bvar$get_posterior()
Examples
spec = specify_bvar$new(us_macro_chan)
post = estimate(spec, 5)
post$get_posterior()

Method get_last_draw()

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

Usage
specify_posterior_bvar$get_last_draw()
Examples
spec = specify_bvar$new(us_macro_chan)
burn = estimate(spec, 5)
post = estimate(burn, 5)

Method clone()

The objects of this class are cloneable with this method.

Usage
specify_posterior_bvar$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Examples

# This is a function that is used within estimate()
spec = specify_bvar$new(us_macro_chan)
post = estimate(spec, 5)
class(post)


## ------------------------------------------------
## Method `specify_posterior_bvar$get_posterior`
## ------------------------------------------------

spec = specify_bvar$new(us_macro_chan)
post = estimate(spec, 5)
post$get_posterior()


## ------------------------------------------------
## Method `specify_posterior_bvar$get_last_draw`
## ------------------------------------------------

spec = specify_bvar$new(us_macro_chan)
burn = estimate(spec, 5)
post = estimate(burn, 5)

R6 Class Representing PriorBVAR

Description

The class PriorBVAR presents a prior specification for the BVAR model.

#' The Model. All the BVAR 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.

This package assumes that the error matrix follows a matrix normal distribution:

E \mid X \sim \mathcal{MN}_{N \times T}(\mathbf{0}, \mathbf{\Sigma}, \mathbf{\Omega})

where \Sigma is the NxN covariance matrix of the error term at time t, and \Omega is a TxT diagonal matrix.

The diagonal elements of \Omega determine the specification of the error term covariance structure. Specifically, the error term at time t follows the multivariate normal distribution

e_t \sim \mathcal{N}_N(\mathbf{0}, \sigma_t^2\lambda_t \mathbf{\Sigma})

where the scalar processes \sigma_t^2 and \lambda_t determine the diagonal elements of \Omega. The process \sigma_t^2 specifies conditional variance and includes three options:

\sigma_t^2 = 1

homoskedastic error term

\sigma_t^2

estimated and following non-centred stochastic volatility

\sigma_t^2

estimated and following centred stochastic volatility

The process \lambda_t specifies the conditional distribution of the error term and includes two options:

\lambda_t = 1

Gaussian error term specification

\lambda_t

estimated and following a priori an inverse gamma 2 distribution \mathcal{IG}2(\nu - 2, \nu), where \nu > 2 is a degrees of freedom parameter

Prior distributions. The autoregressive matrix A is assigned matrix-variate normal distribution:

\mathbf{A} \mid \underline{\mathbf{A}}, \mathbf{V}, \boldsymbol{\Sigma} \sim \mathcal{MN}_{N \times K}(\underline{\mathbf{A}}, \boldsymbol{\Sigma}, \mathbf{V})

with the mean matrix \underline{\mathbf{A}}, and covariance matrices \boldsymbol{\Sigma}_{N\times N} and \mathbf{V}_{K\times K} defining the row- and column-covariance structures.

This is complemented by the inverse Wishart prior for the error term covariance \boldsymbol{\Sigma}:

\boldsymbol{\Sigma} \mid \underline{\mathbf{S}}, \underline{\nu} \sim \mathcal{IW}(\underline{\mathbf{S}}, \underline{\nu})

with the scale matrix \underline{\mathbf{S}} and degrees of freedom \underline{\nu}.

Public fields

A

a real-valued NxK matrix, the mean matrix A_0 of the matrix-variate normal prior distribution for the parameter matrix A.

S

a NxN positive definite scale matrix S_0 of the Inverse Wishart prior distribution for the error term covariance matrix \Sigma.

nu

a positive scalar, shape parameter \nu_0 of the Inverse Wishart prior distribution for the error term covariance matrix \Sigma.

Psi

a KxK scale matrix \Psi_0 of the matrix generalized inverse Gaussian distribution for the equation-specific prior covariance V

Gamma

a KxK scale matrix \Gamma_0 of the matrix generalized inverse Gaussian distribution for the equation-specific prior covariance V

lambda

a positive scalar shape parameter \lambda_0 of the matrix generalized inverse Gaussian distribution for the equation-specific prior covariance V

sv_a

a positive scalar, the shape parameter of the gamma prior in the hierarchical prior for the common stochastic volatility.

sv_s

a positive scalar, the scale parameter of the gamma prior in the hierarchical prior for the common stochastic volatility.

Methods

Public methods

Method new()

Create a new prior specification PriorBVAR.

Usage
specify_prior_bvar$new(
  N,
  p,
  d = 0,
  stationary = rep(FALSE, N),
  is_homoskedastic = TRUE
)
Arguments
N

a positive integer - the number of dependent variables in the model.

p

a positive integer - the autoregressive lag order of the VAR model.

d

a positive integer - the number of exogenous variables in the model.

stationary

an N logical vector - its element set to FALSE sets the prior mean for the autoregressive parameters of the Nth equation to the white noise process, otherwise to random walk.

is_homoskedastic

a logical scalar - if TRUE the model assumes homoskedastic errors, otherwise it assumes stochastic volatility.

Returns

A new prior specification PriorBVAR.

Examples
# a prior for 3-variable example with one lag and stationary data
prior = specify_prior_bvar$new(N = 3, p = 1, stationary = rep(TRUE, 3))
prior$A # show autoregressive prior mean

Method get_prior()

Returns the elements of the prior specification PriorBVAR as a list.

Usage
specify_prior_bvar$get_prior()
Examples
# a prior for 3-variable example with four lags
prior = specify_prior_bvar$new(N = 3, p = 4)
prior$get_prior() # show the prior as list

Method clone()

The objects of this class are cloneable with this method.

Usage
specify_prior_bvar$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Examples

prior = specify_prior_bvar$new(N = 3, p = 1)  # a prior for 3-variable example with one lag
prior$A                                        # show autoregressive prior mean


## ------------------------------------------------
## Method `specify_prior_bvar$new`
## ------------------------------------------------

# a prior for 3-variable example with one lag and stationary data
prior = specify_prior_bvar$new(N = 3, p = 1, stationary = rep(TRUE, 3))
prior$A # show autoregressive prior mean


## ------------------------------------------------
## Method `specify_prior_bvar$get_prior`
## ------------------------------------------------

# a prior for 3-variable example with four lags
prior = specify_prior_bvar$new(N = 3, p = 4)
prior$get_prior() # show the prior as list

R6 Class Representing StartingValuesBVAR

Description

The class StartingValuesBVAR presents starting values for the BVAR model.

Public fields

A

an NxK matrix of starting values for the autoregressive matrix A.

Sigma

an NxN matrix of starting values for the error term covariance \Sigma.

V

a KxK matrix of starting values for the prior equation-specific covariance V of the hierarchical prior distribution for matrix A.

h

an T-vector with the starting values of the log-volatility processes.

rho

a scalalr for the SV autoregressive parameter.

omega

a scalar for the SV process conditional standard deviation.

sigma2v

a scalar for SV process conditional variances.

S

a T integer vector with the auxiliary mixture component indicator.

sigma2_omega

a scalar for the variance of the zero-mean normal prior for \omega.

s_

a positive scalar with the scale of the gamma prior of the hierarchical prior for \sigma^2_{\omega}.

lambda

a T-vetor of starting values for latent variable.

df

a scalar greater than 2 with the starting value for the degrees of freedom parameter of the Student-t conditional distribution of error term.

Methods

Public methods

Method new()

Create new starting values StartingValuesBVAR.

Usage
specify_starting_values_bvar$new(
  N,
  p,
  T,
  d = 0,
  is_homoskedastic = TRUE,
  is_normal = TRUE,
  ar_sigma2 = rep(1, N),
  kappa = c(0.2^2, 10^2)
)
Arguments
N

a positive integer - the number of dependent variables in the model.

p

a positive integer - the autoregressive lag order of the BVAR model.

T

a positive integer - the number of time periods in the data.

d

a positive integer - the number of exogenous variables in the model.

is_homoskedastic

a logical scalar - if TRUE the model assumes homoskedastic errors, otherwise it assumes stochastic volatility.

is_normal

a logical scalar - if TRUE the model assumes normal error term, otherwise, it assumes Student-t errors.

ar_sigma2

a positive N-vector with the autoregressive variance estimates for each variable to be used in the Minnesota prior for the autoregressive parameters.

kappa

a positive 2-vector with the hyperparameters of the Minnesota prior for the autoregressive parameters - the first element is the overall tightness hyperparameter, while the second element is the tightness of the prior on the constant and exogenous variable coefficients.

Returns

Starting values StartingValuesBVAR.

Examples
# starting values for a 3-variable BVAR model
sv = specify_starting_values_bvar$new(N = 3, p = 4, T = 100)

Method get_starting_values()

Returns the elements of the starting values StartingValuesBVAR as a list.

Usage
specify_starting_values_bvar$get_starting_values()
Examples
# starting values for a 3-variable BVAR model
sv = specify_starting_values_bvar$new(N = 3, p = 4, T = 100)
sv$get_starting_values()   # show starting values as list

Method set_starting_values()

Sets the elements of the starting values StartingValuesBVAR to provided values.

Usage
specify_starting_values_bvar$set_starting_values(last_draw)
Arguments
last_draw

a list containing the last draw of elements A - a KxN matrix, Sigma - an NxN matrix, and V - a KxK matrix.

Returns

An object of class StartingValuesBVAR including the last draw of the current MCMC as the starting value to be passed to the continuation of the MCMC estimation using estimate().

Examples
# starting values for a 3-variable BVAR model
sv = specify_starting_values_bvar$new(N = 3, p = 4, T = 100)

# Modify the starting values by:
sv_list = sv$get_starting_values()   # getting them as list
sv_list$A <- matrix(rnorm(12), 3, 4) # modifying the entry
sv$set_starting_values(sv_list)      # providing to the class object

Method clone()

The objects of this class are cloneable with this method.

Usage
specify_starting_values_bvar$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Examples

# starting values for a 3-variable BVAR model.
sv = specify_starting_values_bvar$new(N = 3, p = 4, T = 100)


## ------------------------------------------------
## Method `specify_starting_values_bvar$new`
## ------------------------------------------------

# starting values for a 3-variable BVAR model
sv = specify_starting_values_bvar$new(N = 3, p = 4, T = 100)


## ------------------------------------------------
## Method `specify_starting_values_bvar$get_starting_values`
## ------------------------------------------------

# starting values for a 3-variable BVAR model
sv = specify_starting_values_bvar$new(N = 3, p = 4, T = 100)
sv$get_starting_values()   # show starting values as list


## ------------------------------------------------
## Method `specify_starting_values_bvar$set_starting_values`
## ------------------------------------------------

# starting values for a 3-variable BVAR model
sv = specify_starting_values_bvar$new(N = 3, p = 4, T = 100)

# Modify the starting values by:
sv_list = sv$get_starting_values()   # getting them as list
sv_list$A <- matrix(rnorm(12), 3, 4) # modifying the entry
sv$set_starting_values(sv_list)      # providing to the class object

Provides posterior summary of VAR estimation

Description

Provides posterior mean, standard deviations, as well as 5 and 95 percentiles of the parameters: autoregressive parameters \mathbf{A}, and the covariance matrix \Sigma.

Usage

## S3 method for class 'PosteriorBVAR'
summary(object, ...)

Arguments

object

an object of class PosteriorBVAR obtained using the estimate() function applied to a Bayesian VAR model specification set by function specify_bvar$new() containing draws from the posterior distribution of the parameters.

...

additional arguments affecting the summary produced.

Value

A list reporting the posterior mean, standard deviations, as well as 5 and 95 percentiles of the parameters: autoregressive parameters \mathbf{A}, and the covariance matrix \Sigma..

Author(s)

Tomasz Woźniak wozniak.tom@pm.me

Examples

# simple workflow
############################################################
spec = specify_bvar$new(us_macro_chan)        # specify the model
burn = estimate(spec, 5)                      # run the burn-in
post = estimate(burn, 10)                     # estimate the model
summary(post)

# workflow with the pipe |>
############################################################
us_macro_chan |>
  specify_bvar$new() |>
  estimate(S = 5)  |> 
  estimate(S = 10) |> 
  summary()

A 20-variable US macroeconomic system for the period 1959 Q4 – 2013 Q4

Description

A system of 20 US macroeconomic aggregates used by Chan (2020).

Usage

data(us_macro_chan)

Format

A matrix and a ts object with time series of 217 observations on 20 variables:

rgdp

Real gross domestic product

cpi

Consumer price index

FFR

Effective Federal funds rate

m2

M2 money stock

pinc

Personal income

rpce

Real personal consumption expenditure

ip

Industrial production index

UR

Civilian unemployment rate

hs

Housing starts

pci

Producer price index

pce

Personal consumption expenditures: chain-type price index

ahem

Average hourly earnings: manufacturing

mi

MI money stock

TMR10Y

10-Year Treasury constant maturity rate

rgpdi

Real gross private domestic investment

aetnf

All employees: total nonfarm

pmici

ISM manufacturing: PMI composite index

noi

ISM manufacturing: new orders index

bsro

Business sector: real output per hour of all Persons

sp500

Real stock prices (S& P 500 index divided by PCE index

The series are used and described by Chan (2020) in Appendix B of Supplementary Materials available at <doi:10.1080/07350015.2018.1451336>.

Source

FRED Economic Database, Federal Reserve Bank of St. Louis, https://fred.stlouisfed.org/

References

Chan (2020) Large Bayesian VARs: A Flexible Kronecker Error Covariance Structure, Journal of Business and Economic Statistics, 38(1), 68–79, <doi:10.1080/07350015.2018.1451336>.

Examples

data(us_macro_chan)   # upload the data