SFQRA: Scaled factor-augmented quantile regression with aggregation in conditional mean forecasting

Lei Shu, Yifan Hao, Yu Chen, Qing Yang

Abstract: Achieving robust forecasts for a single time series with many covariates and possible nonlinear effects is a problem worth investigating. In this paper, a scaled factor-augmented quantile regression with aggregation (SFQRA) method is proposed for an effective prediction. It first estimates different conditional quantiles by introducing scaled covariates to the factor-augmented quantile regression, which not only combats the curse of dimensionality but also includes the target information in the estimation. Then the different conditional quantiles are aggregated appropriately to a robust forecast. Moreover, combining SFQRA with feature screening via an aggregated quantile correlation allows it to be extended to handle cases when only a portion of covariates is informative. The effectiveness of the proposed methods is justified theoretically, under the framework of large cross-sections and large time dimensions while no restriction is imposed on the relation between them. Various simulation studies and real data analyses demonstrate the superiority of the newly proposed method in forecasting.