Optimal HAR inference

• Main Author: DOU, Liyu
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2024
• Subjects: heteroskedasticity; autocorrelation; robust inference; maximal persistence; equal-weighted cosine test; Gaussian location model; long-run variance; Student-t adjustment; statistical efficiency; empirical examples; Econometrics; Statistics and Probability
• Online Access: https://ink.library.smu.edu.sg/soe_research/2787; https://ink.library.smu.edu.sg/context/soe_research/article/3786/viewcontent/harinf.pdf
• Institution: Singapore Management University

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.