Predictive quantile regression with mixed roots and increasing dimensions: The ALQR approach

In this paper we propose the adaptive lasso for predictive quantile regression (ALQR). Reflecting empirical findings, allow predictors to have various degrees of persistence and exhibit different signal strengths. The number is allowed grow with sample size. We study regularity conditions under which stationary, local unit root, cointegrated are present simultaneously. next show convergence rates, model selection consistency, asymptotic distributions ALQR. apply proposed method out-of-sample prediction problem stock returns find that it outperforms existing alternatives. also provide numerical evidence from additional Monte Carlo experiments, supporting theoretical results.