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`

- 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

- a finite

#### 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%
[----|----|----|----|----|----|----|----|----|----|
*************************************
```

## 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.

## 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!