What Is a Bayesian VAR?

A Vector Autoregression (VAR) models multiple time series as a system of equations where each variable depends on its own lags and the lags of all other variables in the system.

A Bayesian VAR adds prior distributions over the model parameters. This serves two purposes:

1. Regularization — VARs have many parameters (grows as \(n^2 \times p\) where \(n\) is the number of variables and \(p\) is the lag order). Priors shrink estimates toward sensible values, reducing overfitting.
2. Uncertainty quantification — instead of point estimates, you get a full posterior distribution over coefficients, forecasts, and structural quantities.

When to use a Bayesian VAR

• You have a moderate number of macroeconomic or financial time series (2--20 variables)
• You want probabilistic forecasts with credible intervals
• You want to study how shocks propagate through a system (impulse responses)
• You want to decompose forecast error variance or historical variation by shock source

The Impulso pipeline

Impulso models this as a sequence of immutable types:

VARData -> VAR -> FittedVAR -> IdentifiedVAR

Each step adds information. You cannot skip steps or go backward.