Heteroskedasticity-Autocorrelation Robust Covariance Estimation Under Non-stationary Covariance Processes

The need to estimate variance-covariance matrix in a time series regression arises often in economic applications involving macroeconomic or finance data. In this paper, we study the behavior of two most popular covariance matrix estimators, namely the Kiefer, Vogelsang and Bunzel kernel estimator without truncation (Kiefer, Vogelsang and Bunzel 2000, KVB thereafter) and standard consistent kernel estimators as in Andrews (1991), under the assumption of permanent changes in the covariance process of the regressor and error term. We show that under general form of time-varying covariance structure, KVB statistics no longer have the asymptotic pivotal distributions as claimed. Rather they depend on the covariance process explicitly. On the other hand, the class of traditional heteroskedasticityautocorrelation consistent covariance estimators are still consistent under time-varying covariance. In other words, t-statistic using this class of covariance estimators will have standard normal distribution, at least asymptotically. As more and more researchers switch to KVB from traditional HAC covariance estimators, due to their simplicity and better finite sample performance, this paper point out a source of problems which may arise from using their method. It is not robustness to certain form of heteroskedasticity, namely covariance that changes persistently. We provide brief reviews on empirical evidence of such structures in many macroeconomic and finance data.