Predictive Quantile Regression with Mixed Roots and Increasing Dimensions: The ALQR Approach

TL;DR

This paper introduces the ALQR method, an adaptive lasso approach for predictive quantile regression that handles mixed-root predictors, increasing dimensions, and demonstrates superior out-of-sample stock return predictions.

Contribution

The paper develops ALQR, a novel adaptive lasso technique for quantile regression with mixed persistence predictors and high-dimensional data, including theoretical properties and empirical validation.

Findings

ALQR outperforms existing methods in stock return prediction.

Theoretical convergence rates and model selection consistency are established.

Numerical experiments support the effectiveness of ALQR.

Abstract

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