A new asymptotic theory for heteroskedasticity-autocorrelation robust tests

A new first-order asymptotic theory for heteroskedasticity-autocorrelation (HAC) robust tests based on nonparametric covariance matrix estimators is developed. The bandwidth of the covariance matrix estimator is modeled as a fixed proportion of the sample size. This leads to a distribution theory for HAC robust tests that explicitly captures the choice of bandwidth and kernel. This contrasts with the traditional asymptotics (where the bandwidth increases more slowly than the sample size) where the asymptotic distributions of HAC robust tests do not depend on the bandwidth or kernel. Finite-sample simulations show that the new approach is more accurate than the traditional asymptotics. The impact of bandwidth and kernel choice on size and power of t-tests is analyzed. Smaller bandwidths lead to tests with higher power but greater size distortions, and large bandwidths lead to tests with lower power but smaller size distortions. Size distortions across bandwidths increase as the serial correlation in the data becomes stronger. Overall, the results clearly indicate that for bandwidth and kernel choice there is a trade-off between size distortions and power. Finite-sample performance using the new asymptotics is comparable to the bootstrap, which suggests that the asymptotic theory in this paper could be useful in understanding the theoretical properties of the bootstrap when applied to HAC robust tests.