MCMC Estimation of Bayesian Vectorautoregressions

Efficient Markov Chain Monte Carlo (MCMC) algorithms for the fully Bayesian estimation of vectorautoregressions (VARs) featuring stochastic volatility (SV). Implements state-of-the-art shrinkage priors following Gruber & Kastner (2025) . Efficient equation-per-equation estimation following Kastner & Huber (2020) and Carrerio et al. (2021) .

bayesianVARs

Estimation of Bayesian vectorautoregressions with/without stochastic volatility.

Implements several modern hierarchical shrinkage priors and their semi-global refinements allowing for structured shrinkage. Amongst them Dirichlet-Laplace prior (DL), hierarchical Minnesota prior (HM), Horseshoe prior (HS), normal-gamma prior (NG), $R^2$-induced-Dirichlet-decomposition prior (R2D2) and stochastic search variable selection prior (SSVS).

Concerning the error-term, the user can either specify an order-invariant factor structure or an order-variant cholesky structure.

Installation

Install CRAN version:

install.packages("bayesianVARs")

Install latest development version directly from GitHub:

devtools::install_github("luisgruber/bayesianVARs")

Usage

The main workhorse to conduct Bayesian inference for vectorautoregression models in this package is the function bvar().

Some features:

Prediction, plotting, extraction of model parameters and extraction of fitted values with the usual generic functions predict(), plot(), coef(), vcov() and fitted().
Configure prior distributions with helper functions specify_prior_phi() and specify_prior_sigma().
Computation and simulation of impulse response functions withirf() and specification of structural restrictions with helper function specify_structural_restrictions().

Demonstration

set.seed(537)
# load package
library(bayesianVARs)

# Load data
train_data <-100 * usmacro_growth[1:237,c("GDPC1", "PCECC96", "GPDIC1", "AWHMAN", "GDPCTPI", "CES2000000008x", "FEDFUNDS", "GS10", "EXUSUKx", "S&P 500")]
test_data <-100 * usmacro_growth[238:241,c("GDPC1", "PCECC96", "GPDIC1", "AWHMAN", "GDPCTPI", "CES2000000008x", "FEDFUNDS", "GS10", "EXUSUKx", "S&P 500")]
                                   
# Estimate model using default prior settings
mod <- bvar(train_data, lags = 2L, draws = 2000, burnin = 1000, sv_keep = "all")

# Out of sample prediction and log-predictive-likelihood evaluation
pred <- predict(mod, ahead = 1:4, LPL = TRUE, Y_obs = test_data)

# Visualize in-sample fit plus out-of-sample prediction intervals
plot(mod, predictions = pred)

Documentation

browseVignettes(package = "bayesianVARs")
# If installing directly from GitHub, one has to explicitely request vignettes, e.g. with
# devtools::install_github("luisgruber/bayesianVARs", dependencies = TRUE, build_vignettes = TRUE)