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 use higher-order expansions to provide a size-power frontier for kernel and orthogonal 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 multivariate location model that dominates the theoretical literature, but simulations suggest the qualitative findings extend to stochastic regressors.

Notes: