Complete subset regressions with large-dimensional sets of predictors

Abstract

We analyze the complete subset regression (CSR) approach of Elliott et al. (2013) in situations with many possible predictor variables. The CSR approach has the computational advantage that it can be applied even when the number of predictors exceeds the sample size. Theoretical results establish that the CSR approach achieves variance reduction and Monte Carlo simulations show that it offers a favorable bias–variance trade-off in the presence of many weak predictor variables. Empirical applications to out-of-sample predictability of U.S. unemployment, GDP growth and inflation show that CSR combinations produce more accurate point forecasts than a dynamic factor approach or univariate regressions that do not exploit the information in the cross-section of predictors.