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.