bvars

An R package for Bayesian Forecasting with Large Vector Autoregressions

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), 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), ‘bsvarSIGNs’ by Wang & Woźniak (2025), and ‘bpvars’ by Woźniak (2025) regarding objects, workflows, and code structure, and they constitute an integrated toolset.

Features

Forecasting with Bayesian Vector Autoregressions

• The bvars package includes state-of-the-art Vector Autoregressive models with Minnesota priors and a flexible structure of the error term specification. The model equations are:

       Y = A X + E          (VAR equation)
   E | X ~ MN(0, O, S)      (error term normality)

• dependent variable matrix Y,
• lagged dependent variable matrix X,
• error term E,
• autoregressive parameter matrix A,
• error term covariance matrix S, and
• diagonal matrix O allowing for heteroskedasticity and non-normality of the error term.
• The error terms feature a zero-mean matrix-variate normal distribution with row-specific covariance matrix S and column-specific diagonal covariance matrix O of order T.
• The parameters A and S follow a matrix-variate normal inverse Wishart prior featuring characteristics of the Minnesota priors.
• The diagonal matrix O facilitates the following customisation of the error term specification:
  • conditional multivariate normal or Student’s t distributions,
  • homoskedastic or heteroskedastic specifications with a common volatility modelled by centred or non-centred stochastic volatility.

Simple workflows

• Specify the models using the specify_bvar$new() function
• Estimate the models using the estimate() method
• Predict the future using the forecast() method
• Compute forecast error variance decompositions using function compute_variance_decompositions()
• Use plot() and summary() methods to gain the insights into the core of the empirical problem.

Fast and efficient computations

• Extraordinary computational speed is obtained by combining
  • the application of frontier econometric and numerical techniques, and
  • the algorithms written in C++
• It combines the best of two worlds: the ease of data analysis with R and fast C++ algorithms
• The algorithms used here are very fast. But still, Bayesian estimation might take a little time. Look at our beautiful progress bar in the meantime:

**************************************************|
bvars: Forecasting with Large                     |
       Bayesian Vector Autoregressions            |
**************************************************|
 Gibbs sampler for the BVAR model                 |
**************************************************|
 Progress of the MCMC simulation for 1000 draws
    Every draw is saved via MCMC thinning
 Press Esc to interrupt the computations
**************************************************|
0%   10   20   30   40   50   60   70   80   90   100%
[----|----|----|----|----|----|----|----|----|----|
*************************************

Start your Bayesian analysis of data

The beginnings are as easy as ABC:

library(bvars)                                          # load the package

spec = specify_bvar$new(                                # specify the model
  us_macro_chan,                                        # data
  p = 4,                                                # number of lags
  common_volatility = "ncSV",                           # heteroskedasticity
  distribution = "t",                                   # Student t error term
  stationary = rep(TRUE, ncol(us_macro_chan))           # Minnesota prior spec
)

burn = estimate(spec, S = 10000)                        # run the burn-in
post = estimate(burn, S = 10000)                        # estimate the model
summary(fore)                                           # estimation summary

fore = forecast(                                        # forecast the model 
  post,                                                 # estimation output
  horizon = 6                                           # forecast horizon
)

plot(fore)                                              # plot the forecasts
summary(fore)                                           # forecast summary forecasts

fevd = compute_variance_decompositions(
          post, horizon = 6)                            # compute variance decompositions
plot(fevd)                                              # plot variance decompositions

The bvars package supports a simplified workflow using the |> pipe:

us_macro_chan |>                                        # data
  specify_bvar$new(p = 4) |>                            # specify the model
  estimate(S = 10000) |>                                # run the burn-in
  estimate(S = 10000) -> post                           # estimate the model

post |> forecast(horizon = 6) |> plot()                 # forecasting
post |> compute_variance_decompositions(horizon = 6) |> plot()

Now, you’re ready to analyse your model and forecasts!

The hexagonal logo

This beautiful logo can be reproduced in R using this file.

Resources

• a reference manual
• a website of the family of packages bsvars.org

Installation

The first time you install the package

You must have a cpp compiler. Follow the instructions from Section 1.3. by Eddelbuettel & François (2023). In short, for Windows: install RTools, for macOS: install Xcode Command Line Tools, and for Linux: install the standard development packages.

Once that’s done:

The developer’s version of the package with the newest features can be installed by typing:

devtools::install_github("bsvars/bvars")

Development

The package is under intensive development. Your help is most welcome! Please, have a look at our issues to learn what we’re working on. Thank you!

About the authors

Tomasz is a Bayesian econometrician and a Senior Lecturer at the University of Melbourne. He develops methodology for empirical macroeconomic analyses and programs in R and C++ using Rcpp.