An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator

Abstract

This paper considers a new class of heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimators. The estimators considered are prewhitened kernel estimators with vector autoregressions employed in the prewhitening stage. The paper establishes consistency, rate of convergence, and asymptotic truncated mean squared error (MSE) results for the estimators when a fixed or automatic bandwidth procedure is employed. Conditions are obtained under which prewhitening improves asymptotic truncated MSE. Monte Carlo results show that prewhitening is very effective in reducing bias, improving confidence interval coverage probabilities, and rescuing over-rejection of t-statistics constructed using kernel-HAC estimators. On the other hand, prewhitening is found to inflate variance and MSE of the kernel estimators. Since confidence interval coverage probabilities and over-rejection of t-statistics are usually of primary concern, prewhitened kernel estimators provide a significant improvement over the standard non-prewhitened kernel estimators.