Testing-optimal kernel choice in HAR inference

The paper investigates the optimal kernel choice in heteroskedasticity and autocorrelation robust tests based on the fixed-b asymptotics. In parallel with the optimality of the quadratic spectral kernel under the asymptotic mean squared error criterion of the point estimator of the long run variance as considered in Andrews (1991) , we show that the optimality of the quadratic spectral kernel continues to hold under the testing-oriented criterion of Sun, Philips and Jin (2008) which takes a weighted average of the probabilities of type I and type II errors of the fixed-b asymptotic test.