Macroeconomic forecasting using factor models with martingale difference errors

This paper analyzes the forecasting performance of a new class of factor models with martingale difference errors (FMMDE). The FMMDE makes it possible to retrieve a transformation of the original series so that the resulting variables can be partitioned according to whether they are conditionally mean-independent with respect to past information. Our contribution is twofold. First, we introduce a novel methodology for selecting the number of factors in the FMMDE and demonstrate its finite-sample performance through simulations. Second, we conduct an empirical analysis comparing the FMMDE with alternative methods designed for large datasets to improve predictions of low-frequency macroeconomic aggregates using a comprehensive dataset of monthly U.S. macroeconomic variables. Our results indicate that factor-augmented regressions are particularly effective at predicting real economic variables, with the FMMDE performing well at forecasting industrial production. However, during periods of economic instability, such as during the 2019 coronavirus pandemic, most factor-based methods experienced a decline in predictive accuracy. In such contexts, forecast combination techniques emerge as a more robust alternative, significantly enhancing predictive reliability.