This paper is concerned with the estimation of covariance matrices in the presence of heteroskedasticity and autocorrelation of unknown forms. Currently available estimators that are designed for this context depend upon the choice of a lag truncation parameter and a weighting scheme. Results in the literature provide a condition on the growth rate of the lag truncation parameter as T → ∞ that is suﬀicient for consistency. No results are available, however, regarding the choice of a lag truncation parameter for a ﬁxed sample size, regarding data-dependent automatic lag truncation parameters, or regarding the choice of weighing scheme. In consequence, available estimators are not entirely operational and the relative merits of the estimators are unknown. This paper addresses these problems. Upper and lower bounds on the asymptotic mean squared error of each estimator in a given class are determined and compared. Asymptotically optimal kernel/weighting scheme and bandwidth/lag truncation parameters are obtained using a minimax asymptotic mean squared error criterion. Higher order asymptotically optimal corrections to the ﬁrst order optimal bandwidth/lag truncation parameters are introduced. Using these results, data-dependent automatic bandwidth/lag truncation parameters are deﬁned and are shown to possess certain asymptotic optimality properties. Finite sample properties of the estimators are analyzed via Monte Carlo simulation.
Andrews, Donald W.K., "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation" (1988). Cowles Foundation Discussion Papers. 1120.