Out of Sample Predictability in Predictive Regressions with Many Predictor Candidates

TL;DR

This paper develops a statistical test for detecting out of sample predictability in linear regressions with many predictors, including persistent and stationary series, and introduces a predictor screening method.

Contribution

It proposes a novel out of sample MSE comparison procedure for large predictor sets, with an aggregate test statistic that is standard normal under the null hypothesis.

Findings

The test effectively detects predictability in various predictor types.

The screening procedure identifies the most influential predictors.

Empirical analysis highlights the predictive power of manufacturing new orders.

Abstract

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 implemented in a pairwise manner using one predictor at a time and resulting in an aggregate test statistic that is standard normally distributed under the global null hypothesis of no linear predictability. Predictors can be highly persistent, purely stationary or a combination of both. Upon rejection of the null hypothesis we subsequently introduce a predictor screening procedure designed to identify the most active predictors. An empirical application to key predictors of US economic activity illustrates the usefulness of our methods and highlights the important forward looking role played by the series of manufacturing new orders.