Factor-Augmented Forecasting Subject to Structural Breaks in the Factor Structure
Working Paper, 2026
This paper investigates the impact of structural breaks in the factor structure on factor-augmented forecasting. We decompose the break in the factor loading matrix into rotational and shift components. To effectively utilize pre-break data while maintaining robustness against shift breaks, we propose a novel ``rotated factor’ estimator that minimizes the $L_2$ distance between pre- and post-break loading matrices. We show that the rotated factor estimator achieves the standard convergence rate even under large shift breaks, provided the rotational change is small. Furthermore, we derive the out-of-sample bias–variance trade-offs for competing factor estimators, demonstrating that the rotated factors weakly dominate the conventional full-sample factors by purging shift-break bias, while also outperforming split-sample methods through variance reduction under small rotational changes. To leverage the respective advantages of each estimator in a data-driven way, we introduce a leave-$h$-out cross-validation averaging procedure. Simulations and an empirical application to forecasting post-COVID U.S. macroeconomic data demonstrate that our approach leads to improved forecasting performance and underscores the importance of incorporating structural breaks into factor-augmented models.