Avoiding weak-factor selection in sPCA-based factor-augmented regression: An all subset-averaging perspective

Determining the number of factors and identifying relevant predictive factors in scaled principal component analysis (sPCA)-based regressions remain challenging in the presence of weak factors with minimal pervasiveness and those that are easily obscured by noise. These challenges introduce substantial model uncertainty, often leading to unstable forecasts and degraded predictive accuracy in empirical applications. This paper develops a novel method that combines sPCA-based factor-augmented regressions with all subset averaging (sPCA–ASA) to reduce forecasting uncertainty arising from the joint selection of the number of factors and relevant predictive factors. The sPCA–ASA method relies only on a prespecified maximum number of factors kmax; it models from 1 to kmax factors and equally averages all subset forecasts of sPCA-based factor-augmented regressions. This approach avoids computationally intensive model preselection; does not require consistent estimation of the number of factors, tuning parameters, or optimal weights; and remains robust to weak factors. We also offer a practical guide for selecting kmax. An empirical application to U.S. macroeconomic forecasting demonstrates the superior forecasting performance of sPCA-ASA, substantially reducing forecast errors compared to conventional methods.