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

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().

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>.

Author

Rui Liu rl3023@columbia.edu, Andres Ramirez Hassan aramir21@gmail.com & 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
#> **************************************************|
#> bvars: Forecasting with Large                     |
#>        Bayesian Vector Autoregressions            |
#> **************************************************|
#>  Gibbs sampler for the BVAR model                 |
#> **************************************************|
#>  Progress of the MCMC simulation for 5 draws
#>     Every draw is saved via MCMC thinning
#>  Press Esc to interrupt the computations
#> **************************************************|
post = estimate(burn, 10)                     # estimate the model
#> **************************************************|
#> bvars: Forecasting with Large                     |
#>        Bayesian Vector Autoregressions            |
#> **************************************************|
#>  Gibbs sampler for the BVAR model                 |
#> **************************************************|
#>  Progress of the MCMC simulation for 10 draws
#>     Every draw is saved via MCMC thinning
#>  Press Esc to interrupt the computations
#> **************************************************|

# workflow with the pipe |>
############################################################
us_macro_chan |>
  specify_bvar$new() |>
  estimate(S = 5) |> 
  estimate(S = 10) -> post
#> **************************************************|
#> bvars: Forecasting with Large                     |
#>        Bayesian Vector Autoregressions            |
#> **************************************************|
#>  Gibbs sampler for the BVAR model                 |
#> **************************************************|
#>  Progress of the MCMC simulation for 5 draws
#>     Every draw is saved via MCMC thinning
#>  Press Esc to interrupt the computations
#> **************************************************|
#> **************************************************|
#> bvars: Forecasting with Large                     |
#>        Bayesian Vector Autoregressions            |
#> **************************************************|
#>  Gibbs sampler for the BVAR model                 |
#> **************************************************|
#>  Progress of the MCMC simulation for 10 draws
#>     Every draw is saved via MCMC thinning
#>  Press Esc to interrupt the computations
#> **************************************************|