Optimal HAR inference

This paper considers the problem of deriving heteroskedasticity and autocorrelation robust (HAR) inference about a scalar parameter of interest. The main assumption is that there is a known upper bound on the degree of persistence in data. I derive finite-sample optimal tests in the Gaussian location model and show that the robustness-efficiency tradeoffs embedded in the optimal tests are essentially determined by the maximal persistence. I find that with an appropriate adjustment to the critical value, it is nearly optimal to use the so-called equal-weighted cosine (EWC) test, where the long-run variance is estimated by projections onto q type II cosines. The practical implications are an explicit link between the choice of q and assumptions on the underlying persistence, as well as a corresponding adjustment to the usual Student-t critical value. I illustrate the results in two empirical examples.