HAR Inference for Quantile Regression in Time Series

Jungbin Hwang and Gonzalo Valdés
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Gonzalo Valdés: Universidad de Tarapacá

No 2025-03, Working papers from University of Connecticut, Department of Economics

Abstract: Robust inference in time series quantile regression (QR) poses greater challenges than in conditional mean regression because of nite sample uncertainties arising from two nonparametric components of the asymptotic variance estimator: the conditional QR error density in the Hessian matrix and the long-run variance (LRV) of the non-smooth QR score process. In this paper, we develop a novel QR heteroskedasticity and autocorrelation robust (HAR) inference procedure that integrates an alternative asymptotic inference with an MCMC-based estimator of the inverse QR Hessian. This combination allows us to bypass the kernel-based estimation of the conditional QR density and yields more accurate xed-smoothing asymptotic approximation for the QR Wald statistic. Monte Carlo simulations show that the proposed QR-HAR inference delivers favorable nite sample size control and power compared to exist-ing QR inference in time series. Notably, our QR-HAR inference framework not only applies to existing kernel and orthonormal series (OS) LRV estimators, it also incorporates tuning-parameter-free self-normalized inference without recursive QR parameter estimation.

Keywords: Fixed-b asymptotics; heteroskedasticity and autocorrelation consistency; Laplace-type estimator; nonstandard distributions; testing-optimal smoothing para-meter selection (search for similar items in EconPapers)
JEL-codes: C12 C19 C22 C32 (search for similar items in EconPapers)
Pages: 68 pages
Date: 2025-02, Revised 2026-03
New Economics Papers: this item is included in nep-ecm and nep-ets
Note: Jungbin Hwang is the corresponding author
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