HAC Covariance Matrix Estimation in Quantile Regression

Abstract

This study considers an estimator for the asymptotic variance-covariance matrix in time-series quantile regression models which is robust to the presence of heteroskedasticity and autocorrelation. When regression errors are serially correlated, the conventional quantile regression standard errors are invalid. The proposed solution is a quantile analogue of the Newey-West robust standard errors. We establish the asymptotic properties of the heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimator and provide an optimal bandwidth selection rule. The quantile sample autocorrelation coefficient is biased toward zero in finite sample which adversely affects the optimal bandwidth estimation. We propose a simple alternative estimator that effectively reduces the finite sample bias. Numerical simulations provide evidence that the proposed HAC covariance matrix estimator significantly improves the size distortion problem. We examine the impacts of the expansion of renewable energy resources on electricity prices to illustrate the usefulness of the proposed robust standard error.