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

Rui Fan, Ji Hyung Lee and Youngki Shin

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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.

Date: 2021-01, Revised 2022-12
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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Published in Journal of Econometrics, Vol 237, No 2, Part C, Article 105372, 2023

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Journal Article: Predictive quantile regression with mixed roots and increasing dimensions: The ALQR approach (2023)
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