Bayesian Estimation of Structural Vector Autoregressive Models • 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. 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 complement all this. The implemented techniques align closely with those presented in Lütkepohl, Shang, Uzeda, & Woźniak (2024), Lütkepohl & Woźniak (2020), and Song & Woźniak (2021).

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 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 two more models non-normal structural shocks follow
- 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 heteroskedasticity, non-normality, and hypotheses on autoregressive parameters using functions verify_volatility() 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.

Start your Bayesian analysis of data

The beginnings are as easy as ABC:

library(bsvars)                               # upload the package
data(us_fiscal_lsuw)                          # upload data
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
data(us_fiscal_lsuw)                          # upload data
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 developement 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

The package is under intensive development. Your help is most welcome! Please, have a look at the roadmap, discuss package features and applications, 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 cpp using Rcpp.