Uniform predictive inference for factor models with instrumental and idiosyncratic betas

This paper investigates the impact of allowing for characteristic-based time-varying factor betas on the diffusion-index type forecasts. The factor beta consists of two distinct components: the “instrumental beta” is a function of some observable characteristics, while the “idiosyncratic beta” captures more volatile residual movements. To estimate these characteristic-based time-varying betas and the corresponding factors, we apply the projected principal component analysis (P-PCA) method on high-frequency returns data. The primary advantage of this method is that it refines the estimators of latent factors, which shall be used in the forecasting models. We show that various leading components of the conditional mean forecast error are all asymptotically normal and pairwise independent. Extensive simulation studies show the good finite-sample properties of the P-PCA estimators and demonstrate the advantage of the P-PCA method relative to the classic PCA method in forecasting. In our empirical experiments of volatility prediction, we find that the factor-augmented model associated with the P-PCA method is more parsimonious and achieves better performance for a wide variety of target assets. We also find evidence on different levels of variation over time in the idiosyncratic beta, which necessitates our uniform predictive inference procedure.