Quantile prediction with factor-augmented regression: Structural instability and model uncertainty

The quantile regression is an effective tool in modeling data with heterogeneous conditional distribution. This paper considers the time-varying coefficient quantile predictive regression with factor-augmented predictors, to capture smooth structural changes and incorporate high-dimensional data information in prediction simultaneously. Uniform consistency of the local linear quantile coefficient estimators is established under misspecification. To further improve the forecast accuracy, a novel time-varying model averaging based on local forward-validation is developed. The averaging estimator is shown to be asymptotically optimal in the sense of minimizing out-of-sample forecast risk function. Furthermore, the weight selection consistency and the asymptotic distribution of the averaging coefficient estimator are established. Numerical results from simulations and a real data application to forecasting U.S. inflation demonstrate the nice performance of the averaging estimators.