The Size-Power Tradeoff in HAR Inference

• 成果类型: Article
• 署名作者: Lazarus, Eben; Lewis, Daniel J.; Stock, James H.
• 署名单位: Massachusetts Institute of Technology (MIT); Federal Reserve System - USA; Federal Reserve Bank - New York; Harvard University; National Bureau of Economic Research
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.3982/ECTA15404
• 发表日期: 2021
• 页码: 2497-2516
• 关键词: SPECTRAL DENSITY; Standard errors; heteroskedasticity; selection; asymptotics; tests

摘要

Heteroskedasticity- and autocorrelation-robust (HAR) inference in time series regression typically involves kernel estimation of the long-run variance. Conventional wisdom holds that, for a given kernel, the choice of truncation parameter trades off a test's null rejection rate and power, and that this tradeoff differs across kernels. We formalize this intuition: using higher-order expansions, we provide a unified size-power frontier for both kernel and weighted orthonormal series tests using nonstandard fixed-b critical values. We also provide a frontier for the subset of these tests for which the fixed-b distribution is t or F. These frontiers are respectively achieved by the QS kernel and equal-weighted periodogram. The frontiers have simple closed-form expressions, which show that the price paid for restricting attention to tests with t and F critical values is small. The frontiers are derived for the Gaussian multivariate location model, but simulations suggest the qualitative findings extend to stochastic regressors.