Forecasting VARs, model selection, and shrinkage

This paper provides an empirical comparison of various selection and penalized regression approaches for forecasting with vector autoregressive systems. In particular, we investigate the effect of the system size as well as the effect of various prior specification choices on the relative and overall forecasting performance of the methods. The data set is a typical macroeconomic quarterly data set for the US. We find that these specification choices are crucial for most methods. Conditional on certain choices, the variation across different approaches is relatively small. There are only a few methods which are not competitive under any scenario. For single series, we find that increasing the system size can be helpful - depending on the employed shrinkage method.