Uniform Predictive Inference for Factor Models with Instrumental and Idiosyncratic Betas

This paper investigates the effect of characteristic-based time-varying factor beta on the diffusion-index type forecast. Specifically, the factor beta includes two distinct components: the "instrumental beta'' is a function of some observed stable variables, while the "idiosyncratic beta'' captures the more volatile residual movements. To estimate these time-varying beta's, we propose to apply the projected PCA (P-PCA), which takes advantage of firm characteristics, on high-frequency return data. We show that various components of the conditional mean forecast error are all asymptotically normal. Of particular note is that the time-varying idiosyncratic beta has nontrivial effects on the first-order asymptotic of the conditional mean forecast. A Monte Carlo exercise demonstrates fairly good finite sample properties of the P-PCA estimators and shows that the P-PCA method largely outperforms the traditional PCA method for factor-augmented prediction. In our empirical experiments of volatility forecasting, we find that the predictive model estimated by the P-PCA method achieves preferable performance for a wide variety of target assets. We provide evidence that the forecast uncertainty arose from the time variation in factor beta magnifies during volatile periods. In such cases, exploiting the information in stable characteristics plays an even more crucial role in producing effective diffusion-index forecasts