HAC Covariance Matrix Estimation in Quantile Regression

This study considers an estimator for the asymptotic variance-covariance matrix in time-series quantile regression models which is robust to the presence of heteroscedasticity 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 heteroscedasticity 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. To illustrate the usefulness of the proposed robust standard error, we examine the impacts of the expansion of renewable energy resources on electricity prices. Supplementary materials for this article are available online.

本研究针对时间序列分位数回归（quantile regression）模型中的渐近方差-协方差矩阵，构建了一种对异方差性（heteroscedasticity）与自相关（autocorrelation）具备稳健性的估计量。当回归误差存在序列自相关时，传统分位数回归的标准误不再具备有效性。本文所提出的解决方案，是纽威-韦斯特（Newey-West）稳健标准误在分位数回归场景下的对应形式。本文推导了异方差与自相关一致（heteroscedasticity and autocorrelation consistent, HAC）协方差矩阵估计量的渐近性质，并给出了最优带宽选择准则。有限样本下，分位数样本自相关系数存在向零收敛的偏倚，这会对最优带宽的估计造成不利影响。为此本文提出一种简易的替代估计量，可有效降低有限样本偏倚。数值模拟结果证实，本文提出的HAC协方差矩阵估计量可显著改善尺度扭曲问题。为验证所提出的稳健标准误的应用价值，本文考察了可再生能源资源扩张对电力价格的影响。本文的补充材料可在线获取。