Forecasting in vector autoregressions with many predictors

This paper addresses the issue of improving the forecasting performance of vector autoregressions (VARs) when the set of available predictors is inconveniently large to handle with methods and diagnostics used in traditional small scale models. First, available information from a large dataset is summarized into a considerably smaller set of variables through factors estimated using standard principal components. However, even in the case of reducing the dimension of the data the true number of factors may still be large. For that reason I introduce in my analysis simple and efficient Bayesian model selection methods. Model estimation and selection of predictors is carried out automatically through a stochastic search variable selection (SSVS) algorithm which requires minimal input by the user. I apply these methods to forecast 8 main U.S. macroeconomic variables using 124 potential predictors. I find improved out of sample fit in high dimensional specifications that would otherwise suffer from the proliferation of parameters.