Econometrica: Jan 2008, Volume 76, Issue 1
Optimal Bandwidth Selection in Heteroskedasticity–Autocorrelation Robust Testing
Yixiao Sun, Peter C. B. Phillips, Sainan JinThis paper considers studentized tests in time series regressions with nonparametrically autocorrelated errors. The studentization is based on robust standard errors with truncation lag = for some constant ∈(0, 1] and sample size . It is shown that the nonstandard fixed‐ limit distributions of such nonparametrically studentized tests provide more accurate approximations to the finite sample distributions than the standard small‐ 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) confirm that the new plug‐in procedure works well in finite samples.
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