Lazarus, Eben; Lewis, Daniel J; Stock, James H; (2021) The Size‐Power Tradeoff in HAR Inference. Econometrica , 89 (5) pp. 2497-2516. 10.3982/ecta15404.

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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 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.

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