Combining Shrinkage and Sparsity in Conjugate Vector Autoregressive Models

Document pages: 35 pages

Abstract: Conjugate priors allow for fast inference in large dimensional vectorautoregressive (VAR) models but, at the same time, introduce the restrictionthat each equation features the same set of explanatory variables. This paperproposes a straightforward means of post-processing posterior estimates of aconjugate Bayesian VAR to effectively perform equation-specific covariateselection. Compared to existing techniques using shrinkage alone, our approachcombines shrinkage and sparsity in both the VAR coefficients and the errorvariance-covariance matrices, greatly reducing estimation uncertainty in largedimensions while maintaining computational tractability. We illustrate ourapproach by means of two applications. The first application uses syntheticdata to investigate the properties of the model across differentdata-generating processes, the second application analyzes the predictive gainsfrom sparsification in a forecasting exercise for US data.