Prediction When Factors are Weak

In economic forecasting, principal component analysis (PCA) has been the most prevalent approach to the recovery of factors, which summarize information in a large set of predictors. Nevertheless, the theoretical justification of this approach often relies on a convenient and critical assumption that factors are pervasive. To incorporate information from weaker factors, we propose a new prediction procedure based on supervised PCA, which iterates over selection, PCA, and projection. The selection step finds a subset of predictors most correlated with the prediction target, whereas the projection step permits multiple weak factors of distinct strength. We justify our procedure in an asymptotic scheme where both the sample size and the cross-sectional dimension increase at potentially different rates. Our empirical analysis highlights the role of weak factors in predicting inflation, industrial production growth, and changes in unemployment.