HAR Inference for Quantile Regression in Time Series

This paper develops robust inference for conditional quantile regression (QR) under unknown forms of weak dependence in time series data. We rst establish xed-smoothing asymptotic theory for QR by showing that the long-run variance (LRV) estimator for the non-smooth QR score process weakly converges to a random matrix scaled by the true LRV. Additionally, QR-Wald statistics based on the kernel LRV estimator converge to non-standard limits, while using orthonormal series LRV estimators yields standard F and t limits. For the practical implementation of our new asymptotic theory for Wald and t inference in QR, we extend heteroskedasticity and autocorrelation robust (HAR) inference for conditional mean regression to QR and apply the optimal smoothing parameter selection rule based on the Neyman-Pearson principle. Monte Carlo simulation results show that our QR-HAR procedure reduces size distortions of the HAR inference based on the conditional mean regression and the QR-HAC inference particularly in scenarios with moderate sample sizes, strong temporal dependence, and multiple parameters in the joint null hypothesis.