Forecasting with supervised factor models

A conventional approach to forecast in a data-rich environment is to estimate factor-augmented predictive regressions with factors constructed by principal component analysis. This study analyzes under which circumstances gains in forecast accuracy can be achieved by incorporating some form of supervision in the factor estimation process. Specifically, principal covariate regression (PCovR) is considered. For the problem of choosing a value for the supervision parameter in PCovR, an information criterion is proposed. The information criterion is shown to be an appropriate means to find a good balance between predictor space compression and target orientation of the estimated factors. A simulation study and an empirical application on a macroeconomic dataset show that supervised factors can improve the forecasting accuracy of factor models.