Consistent model selection for factor-augmented regressions

Factor-augmented regression (FAR) is an effective tool in forming predictions in the presence of big data sets. However, few studies have considered the selection of latent factors and observed covariates simultaneously in FAR. This paper addresses this issue and introduces a new set of information criteria for factor selection and covariate selection jointly. In particular, we demonstrate that the factor estimation error will not only influence the factor selection, but also the covariate selection in FAR. As a result, the penalty used to ensure consistent model selection should depend on both the cross-sectional dimension and the time length, to account for the effect of factor estimation error. Selection consistency is then proved under standard regularity conditions. The simulation results demonstrate the nice performance of the proposed criteria.