Predictive Quantile Regression with Mixed Roots and Increasing Dimensions

In this paper we study the benefit of using the adaptive LASSO for predictive quantile regression. It is common that predictors in predictive quantile regression have various degrees of persistence and exhibit different signal strengths in explaining the dependent variable. We show that the adaptive LASSO has the consistent variable selection and the oracle properties under the simultaneous presence of stationary, unit root and cointegrated predictors. Some encouraging simulation and out-of-sample prediction results are reported.