Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing

In time series regressions with nonparametrically autocorrelated errors, it is now standard empirical practice to use kernel-based robust standard errors that involve some smoothing function over the sample autocorrelations. The underlying smoothing parameter b, which can be defined as the ratio of the bandwidth (or truncation lag) to the sample size, is a tuning parameter that plays a key role in determining the asymptotic properties of the standard errors and associated semi-parametric tests. Small-b asymptotics involve standard limit theory such as standard normal or chi-squared limits, whereas fixed-b asymptotics typically lead to nonstandard limit distributions involving Brownian bridge functionals. The present paper shows that the nonstandard fixed-b limit distributions of such nonparametrically studentized tests provide more accurate approximations to the finite sample distributions than the standard small-b limit distribution. In particular, using asymptotic expansions of both the finite sample distribution and the nonstandard limit distribution, we confirm that the second-order corrected critical value based on the expansion of the nonstandard limiting distribution is also second-order correct under the standard small-b asymptotics. We further show that, for typical economic time series, the optimal bandwidth that minimizes a weighted average of type I and type II errors is larger by an order of magnitude than the bandwidth that minimizes the asymptotic mean squared error of the corresponding long-run variance estimator. A plug-in procedure for implementing this optimal bandwidth is suggested and simulations confirm that the new plug-in procedure works well in finite samples