Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing

The paper considers studentized tests in time series regressions with nonparametrically autocorrelated errors. The studentization is based on robust standard errors with truncation lagM = bT for some constant b 2 (0; 1] and sample size T: It is shown that the nonstandard …xed-b limit distributions of such nonparametrically studentized tests provide more accurate approximations to the …nite sample distributions than the standard small-b limit distribution. 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 (not reported here) con…rm that the new plug-in procedure works well in …nite samples. Keywords: Asymptotic expansion, bandwidth choice, kernel method, long-run variance, loss function, nonstandard asymptotics, robust standard error, Type I and Type II errors An earlier version of the paper is available as Sun, Phillips and Jin (2006). The present version is a substantially shorter paper and readers are referred to the earlier version for further details, discussion, proofs, and some asymptotic expansion results of independent interest. The authors thank Whitney Newey, two anonymous referees, and many seminar participants for comments on earlier versions. Phillips acknowledges partial research support from the Kelly Foundation and the NSF under Grant No. SES 04-142254. Jin acknowledges …nancial support from the NSFC (Grant No. 70601001). We thank Maarten van Kampen for pointing out a calculation error and a typo in the third order expansion after the paper was published.