The Size-Power Tradeoff in HAR Inference
32 Pages Posted: 15 Aug 2019 Last revised: 18 Jan 2021
Date Written: January 17, 2021
Abstract
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 upon evaluation 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.
Keywords: heteroskedasticity- and autocorrelation-robust estimation, HAR, long-run variance estimator
JEL Classification: C22, C32
Suggested Citation: Suggested Citation