Forecasting Using Supervised Factors and Idiosyncratic Elements

We extend the Three-Pass Regression Filter (3PRF) in two dimensions. First, we allow the factors driving the predictor panel to be weak. Second, we allow the idiosyncratic components of the predictors to contain additional predictive information for the forecasting target. We establish conditions under which 3PRF consistently recovers the target-relevant factor space under weak factor structures and characterize how its convergence rate depends on the relative strength of relevant and irrelevant factors. Stronger relevant factors improve the rate at which 3PRF approaches the infeasible factor forecast, whereas stronger irrelevant factors have the opposite effect. We use these results to compare 3PRF with Principal Component Regression (PCR) and identify settings in which either procedure has a relative advantage. To accommodate predictive information outside the common factor space, we augment 3PRF with a Least Absolute Shrinkage and Selection Operator (LASSO) regression on estimated idiosyncratic components, yielding the 3PRF LASSO estimator. We derive its prediction-error rate while accounting for the fact that the idiosyncratic regressors are generated from a first-stage factor estimator. Monte Carlo simulations support the asymptotic results and indicate strong finite-sample forecasting performance of 3PRF LASSO. In an empirical application involving forecasts of U.S. headline CPI inflation using FRED-QD data, 3PRF LASSO delivers competitive forecast performance.