A new robust inference for predictive quantile regression

This paper proposes a novel approach to offer robust inferential theory across all types of persistent regressors in predictive quantile regression model. We first estimate with an auxiliary regressor, which is generated as weighted combination exogenous random walk process and bounded transformation the original regressor. With similar spirit rotation factor analysis, one can then construct estimator using estimated coefficients predictor Under some mild conditions, it shows that self-normalized test statistic based on converges standard normal distribution. Our new enjoys good property reach local power under optimal rate T nonstationary for stationary predictor, respectively. More importantly, our be easily used characterize mixed persistency degrees multiple regressions. Simulations empirical studies are provided demonstrate effectiveness newly proposed approach. The heterogeneous predictability US stock returns at different levels reexamined.