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

arXiv: https://arxiv.org/abs/2101.11568 · HTML: https://mlsanity.com/paper/2101.11568/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2021.

## Built on by (most cited first, 1 of 1)

- [On LASSO for High Dimensional Predictive Regression](https://mlsanity.com/paper/2212.07052/) (2022)

## Abstract (arXiv)

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.