Bayesian Estimation of Structural Vector Autoregressive Models

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) complement all this. The implemented techniques align closely with those presented in Lütkepohl, Shang, Uzeda, & Woźniak (2025) , Lütkepohl & Woźniak (2020) , and Song & Woźniak (2021) 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) , 'bvars' by Liu, Ramirez Hassan, Woźniak (2026) , and 'bpvars' by Woźniak (2026) , and they constitute an integrated toolset.

bsvars

An R package for Bayesian Estimation of Structural Vector Autoregressive Models

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) complement all this. The implemented techniques align closely with those presented in Lütkepohl, Shang, Uzeda, & Woźniak (2025), Lütkepohl & Woźniak (2020), and Song & Woźniak (2021) 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), ‘bvars’ by Liu, Ramirez Hassan, Woźniak (2026), and ‘bpvars’ by Woźniak (2026), and they constitute an integrated toolset.

Features

Structural Vector Autoregressions

• All the models in the bsvars package consist of the Vector Autoregressive equation, with autoregressive parameters A and error terms E, and the structural equation with a structural matrix B and shocks U

    Y = AX + E           (VAR equation)
   BE = U                (structural equation)

• The models are identified via exclusion restrictions, heteroskedasticity, or non-normality
• The autoregressive parameters A and the structural matrix B may include exclusion restrictions and feature a three-level local-global hierarchical prior that estimates the equation-specific level of shrinkage
• In five models the structural shocks are conditionally normal with zero mean and diagonal covariance matrix with variances that are:
  • equal to one, that is, time invariant
  • time-varying following non-centred Stochastic Volatility
  • time-varying following centred Stochastic Volatility
  • time-varying with stationary Markov Switching
  • time-varying with sparse Markov Switching where the number of volatility regimes is estimated
• In three more models non-normal structural shocks follow
  • a joint Student-t distribution with estimated equation-specific degrees-of-freedom parameter
  • a finite mixture of normal components and component-specific variances
  • a sparse mixture of normal components and component-specific variances where the number of states is estimated

Simple workflows

• Specify the models using specify_bsvar_* functions, for instance, specify_bsvar_sv$new()
• Estimate the models using the estimate() method
• Predict the future using the forecast() method
• Provide structural analyses using impulse responses, forecast error variance decompositions, historical decompositions, and structural shocks using functions compute_impulse_responses(), compute_variance_decompositions(), compute_historical_decompositions(), and compute_structural_shocks() respectively
• Analyse the fitted values, time-varying volatility, and volatility regimes using functions compute_fitted_values(), compute_conditional_sd(), and compute_regime_probabilities() respectively
• Use plot() and summary() methods to gain the insights into the core of the empirical problem.
• Verify identification through heteroskedasticity, non-normality, and hypotheses on autoregressive parameters using functions verify_identification() and verify_autoregression()

Fast and efficient computations

• Extraordinary computational speed is obtained by combining
  • the application of frontier econometric and numerical techniques, and
  • the implementation using compiled code written in cpp
• It combines the best of two worlds: the ease of data analysis with R and fast cpp 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:

**************************************************|
bsvars: Bayesian Structural Vector Autoregressions|
**************************************************|
 Gibbs sampler for the SVAR-SV model              |
   Non-centred SV model is estimated              |
**************************************************|
 Progress of the MCMC simulation for 1000 draws
    Every 10th draw is saved via MCMC thinning
 Press Esc to interrupt the computations
**************************************************|
0%   10   20   30   40   50   60   70   80   90   100%
[----|----|----|----|----|----|----|----|----|----|
*************************************

The hexagonal logo

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

Resources

• a vignette by Woźniak (2024)
• a reference manual
• a website of the family of packages bsvars.org
• bsvars on CRAN
• youtube recordings:
  • Workshop on Open Source Forecasting youtube recording
  • Forecasting for Social Good youtube recording
  • Workshops for Ukraine youtube recording
• presentations:
  • IIF Workshop on Open Source Forecasting 2025-06 featuring bsvars 3.2
  • for students at Szkoła Główna Handlowa given in Warsaw in December 2024 featuring bsvars 3.2 and bsvarSIGNs 1.0.1]
  • at Uniwersytet Warszawski given in Warsaw in December 2024 featuring bsvars 3.2 and bsvarSIGNs 1.0.1
  • for students and researchers at Uniwersytet Ekonomiczny w Krakowie given in Kraków in December 2024 featuring bsvars 3.2 and bsvarSIGNs 1.0.1
  • for Bayesian Econometrics students at the University of Melbourne given in October 2024 featuring bsvars 3.1
  • for the QuantEcon lab at the Australian National University given in August 2024 featuring bsvars 3.1 and bsvarSIGNs 1.0.1
  • at Monash University given in August 2024 featuring bsvars 3.1 and bsvarSIGNs 1.0
  • for Workshops for Ukraine given in August 2024 featuring bsvars 3.1
  • for Macroeconometrics students at the University of Melbourne given in May 2024 featuring bsvars 2.1.0

Start your Bayesian analysis of data

The beginnings are as easy as ABC:

library(bsvars)                               # upload the package
spec      = specify_bsvar_sv$new(us_fiscal_lsuw, p = 4)   # specify the model
burn_in   = estimate(spec, 1000)              # run the burn-in
out       = estimate(burn_in, 50000)          # estimate the model

fore      = forecast(out, horizon = 8)        # forecast 2 years ahead
plot(fore)                                    # plot the forecast

irfs      = compute_impulse_responses(out, 8) # compute impulse responses  
plot(irfs)                                    # plot the impulse responses

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

library(bsvars)                               # upload the package
us_fiscal_lsuw |>
  specify_bsvar_sv$new(p = 4) |>              # specify the model
  estimate(S = 1000) |>                       # run the burn-in
  estimate(S = 50000) -> out                  # estimate the model

out |> forecast(horizon = 8) |> plot()        # compute and plot forecasts
out |> compute_impulse_responses(8) |> plot() # compute and plot impulse responses

Now, you’re ready to analyse your model!

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:

Just open your R and type:

install.packages("bsvars")

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

devtools::install_github("bsvars/bsvars")

Development

Your help is most welcome! Contribute by submitting a Pull Request with your code. Contributions that add new functionality require prior agreement with the package authors. We only accept submissions from humans, and AI agents cannot be listed as contributors. This means that the person providing the code takes full responsibility for the contribution. Please also have a look at the roadmap, or report a bug. Thank you!

About the author

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.