Higher-Order Improvements of the Parametric Bootstrap for Long-Memory Gaussian Processes

43 Pages Posted: 29 Aug 2002

See all articles by Donald W. K. Andrews

Donald W. K. Andrews

Yale University - Cowles Foundation

Offer Lieberman

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management

Date Written: August 2003

Abstract

This paper determines coverage probability errors of both delta method and parametric bootstrap confidence intervals (CIs) for the covariance parameters of stationary long-memory Gaussian time series. CIs for the long-memory parameter d_{0} are included. The results establish that the bootstrap provides higher-order improvements over the delta method. Analogous results are given for tests. The CIs and tests are based on one or other of two approximate maximum likelihood estimators. The first estimator solves the first-order conditions with respect to the covariance parameters of a "plug-in" log-likelihood function that has the unknown mean replaced by the sample mean. The second estimator does likewise for a plug-in Whittle log-likelihood. The magnitudes of the coverage probability errors for one-sided bootstrap CIs for covariance parameters for long-memory time series are shown to be essentially the same as they are with iid data. This occurs even though the mean of the time series cannot be estimated at the usual n^{1/2} rate.

Keywords: Asymptotics, Confidence Intervals, Delta Method, Edgeworth Expansion, Gaussian Process, Long Memory, Maximum Likelihood Estimator, Parametric Bootstrap, t Statistic, Whittle Likelihood

JEL Classification: C12, C13, C15

Suggested Citation

Andrews, Donald W. K. and Lieberman, Offer, Higher-Order Improvements of the Parametric Bootstrap for Long-Memory Gaussian Processes (August 2003). Available at SSRN: https://ssrn.com/abstract=323604

Donald W. K. Andrews (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3698 (Phone)
203-432-6167 (Fax)

Offer Lieberman

Technion-Israel Institute of Technology - The William Davidson Faculty of Industrial Engineering & Management ( email )

Haifa 32000
Israel
973 4 8294438 (Phone)
972 4 8235194 (Fax)

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