Predictive Quantile Regression with High-Dimensional Predictors: The Variable Screening Approach

TL;DR

This paper improves variable screening for high-dimensional data in quantile regression, especially for time-series, demonstrating its effectiveness through simulations and real-world growth-at-risk forecasting with richer datasets.

Contribution

It refines the QPC-based screening method for $eta$-mixing time-series, providing new convergence bounds and validating performance with simulations and empirical growth-at-risk forecasts.

Findings

QPC screening performs well under weak dependence.

Labor market factors are key predictors for growth-at-risk.

Using richer datasets improves forecasting accuracy.

Abstract

This paper advances a variable screening approach to enhance conditional quantile forecasts using high-dimensional predictors. We have refined and augmented the quantile partial correlation (QPC)-based variable screening proposed by Ma et al. (2017) to accommodate $\beta$-mixing time-series data. Our approach is inclusive of i.i.d scenarios but introduces new convergence bounds for time-series contexts, suggesting the performance of QPC-based screening is influenced by the degree of time-series dependence. Through Monte Carlo simulations, we validate the effectiveness of QPC under weak dependence. Our empirical assessment of variable selection for growth-at-risk (GaR) forecasting underscores the method's advantages, revealing that specific labor market determinants play a pivotal role in forecasting GaR. While prior empirical research has predominantly considered a limited set of predictors, we employ the comprehensive Fred-QD dataset, retaining a richer breadth of information for GaR forecasts.