Supervision in Factor Models Using a Large Number of Predictors

In this paper we investigate the forecasting performance of a particular factor model (FM) in which the factors are extracted from a large number of predictors. We use a semi-parametric state-space representation of the FM in which the forecast objective, as well as the factors, is included in the state vector. The factors are informed of the forecast target (supervised) through the state equation dynamics. We propose a way to assess the contribution of the forecast objective on the extracted factors that exploits the Kalman filter recursions. We forecast one target at a time based on the filtered states and estimated parameters of the state-space system. We assess the out-of-sample forecast performance of the proposed method in a simulation study and in an empirical application, comparing its forecasts to the ones delivered by other popular multivariate and univariate approaches, e.g. a standard dynamic factor model with separate forecast and state equations.