Predictive Regressions: A Machine Learning Perspective

Abstract

In this article, we quantify the forecasting efficiency of the OLS estimator in uni-variate predictive regressions. We link the prediction accuracy to three key quantities: the persistence of the underlying series, the forecasting horizon, and the sample size. We find that high auto-correlation in the dependent variable is required to reach reasonably low levels of mean squared errors. In this case, we identify two configurations which generate positive out-of-sample R-squared: short term forecasting with small samples and long horizon predictions with very deep samples. Two examples of such configurations can easily be found in financial economics: the short term volatility and the long term equity premium. We confirm our results via an empirical study on the SP 500 with a series of 15 popular predictors used in the literature.

Keywords: Asset Pricing, Predictive Regression, Machine Learning, Estimator Efficiency

JEL Classification: G11, G12, C53, C22