Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing

• Main Authors: SUN, Yixiao, PHILLIPS, Peter C. B., JIN, Sainan
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2008
• Subjects: Asymptotic expansion; bandwidth choice; kernel method; long-run variance; loss function; nonstandard asymptotics; robust standard error; Type I and Type II errors; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/61; https://ink.library.smu.edu.sg/context/soe_research/article/1060/viewcontent/HAR_testing_av.pdf
• Institution: Singapore Management University

This paper considers studentized tests in time series regressions with nonparametrically autocorrelated errors. The studentization is based on robust standard errors with truncation lag M = bT for some constant b ∈ (0, 1] and sample size T. It is shown 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. 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.