Optimal HAR inference - DOU, Liyu (Institutional Knowledge at Singapore Management University, 2024)
This paper addresses the problem of deriving heteroskedasticity and autocorrelation robust (HAR) inference for a scalar parameter of interest, under the assumption of a known upper bound on data persistence. Finite-sample optimal tests are derived within the Gaussian location model, revealing that robustness-efficiency tradeoffs are primarily determined by the maximal persistence. With a suitable adjustment to the critical value, the equal-weighted cosine (EWC) test emerges as nearly optimal, wherein the long-run variance is estimated through projections onto q type II cosines. This approach establishes a direct link between the choice of q and persistence assumptions, accompanied by adjustments to the conventional Student-t critical value. The findings are demonstrated through two empirical examples.