This paper reviews estimation and forecasting with Bayesian vector autoregressions (BVARs). In the first part of the paper, we propose a clear classification of the most frequently used prior distributions and we show how the parameters of posterior distributions can be computed for the priors we consider in the paper. A separate section describes the endogenous choice of prior hyperparameters that is currently a key step to estimate a BVAR in a data-rich environment.
The second part of this paper is devoted to forecasting with BVARs. We review both point and density forecasting.
We also developed a package bvarr for statistical environment R with the same notations as in this review. The bvarr package can be freely used for research and educational purposes.