Improved Har Inference Using Power Kernels Without Truncation

52 Pages Posted: 11 Jun 2005

See all articles by Peter C. B. Phillips

Peter C. B. Phillips

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

Yixiao Sun

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

Sainan Jin

Peking University - Guanghua School of Management

Date Written: May 2005

Abstract

Employing power kernels suggested in earlier work by the authors (2003), this paper shows how to refine methods of robust inference on the mean in a time series that rely on families of untruncated kernel estimates of the long-run parameters. The new methods improve the size properties of heteroskedastic and autocorrelation robust (HAR) tests in comparison with conventional methods that employ consistent HAC estimates, and they raise test power in comparison with other tests that are based on untruncated kernel estimates. Large power parameter (p) asymptotic expansions of the nonstandard limit theory are developed in terms of the usual limiting chi-squared distribution, and corresponding large sample size and large p asymptotic expansions of the finite sample distribution of Wald tests are developed to justify the new approach. Exact finite sample distributions are given using operational techniques. The paper further shows that the optimal p that minimizes a weighted sum of type I and II errors has an expansion rate of at most O (T1/2) and can even be O (1) for certain loss functions, and is therefore slower than the O (T2/3) rate which minimizes the asymptotic mean squared error of the corresponding long run variance estimator. A new plug-in procedure for implementing the optimal p is suggested. Simulations show that the new plug-in procedure works well infinite samples.

Keywords: Asymptotic expansion, consistent HAC estimation, data-determined kernel estimation, exact distribution, HAR inference, large p asymptotics, long run variance, loss function, power parameter, sharp origin kernel.

JEL Classification: C13, C14, C22, C51

Suggested Citation

Phillips, Peter C. B. and Sun, Yixiao and Jin, Sainan, Improved Har Inference Using Power Kernels Without Truncation (May 2005). Available at SSRN: https://ssrn.com/abstract=740347

Peter C. B. Phillips (Contact Author)

University of Auckland Business School ( email )

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Yixiao Sun

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

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Sainan Jin

Peking University - Guanghua School of Management ( email )

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