Out of sample predictability in predictive regressions with many predictor candidates

This paper is concerned with detecting the presence of out of sample predictability in linear predictive regressions with a potentially large set of candidate predictors. We propose a procedure based on out of sample MSE comparisons that is implementedin a pairwise manner using one predictor at a time and resulting in an aggregate test statistic that is standard normally distributed under the none hypothesis of no linear predictability. Predictors can be highly persistent, purely stationary or a combination of both. Upon rejection of the none hypothesis we subsequently introduce a predictor screening procedure designed to identify the most active predictors.