Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing

52 Pages Posted: 4 Jan 2006

See all articles by Yixiao Sun

Yixiao Sun

University of California, San Diego (UCSD) - Department of Economics

Peter C. B. Phillips

University of Auckland Business School; Yale University - Cowles Foundation; Singapore Management University - School of Economics

Sainan Jin

Peking University - Guanghua School of Management

Date Written: January 2006

Abstract

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.

Keywords: Asymptotic expansion, bandwidth choice, kernel method, long-run variance, loss function, nonstandard asymptotics, robust standard error, Type I and Type II errors

JEL Classification: C13, C14, C22, C51

Suggested Citation

Sun, Yixiao and Phillips, Peter C. B. and Jin, Sainan, Optimal Bandwidth Selection in Heteroskedasticity-Autocorrelation Robust Testing (January 2006). Cowles Foundation Discussion Paper No. 1545, Available at SSRN: https://ssrn.com/abstract=873624

Yixiao Sun

University of California, San Diego (UCSD) - Department of Economics ( email )

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Peter C. B. Phillips (Contact Author)

University of Auckland Business School ( email )

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Yale University - Cowles Foundation ( email )

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Singapore Management University - School of Economics

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Sainan Jin

Peking University - Guanghua School of Management ( email )

Peking University
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