Higher-order Improvements of the Parametric Bootstrap for Long-memory Gaussian Processes

Donald W. K. Andrews () and Offer Lieberman
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Offer Lieberman: Technion-Israel Institute

No 1378, Cowles Foundation Discussion Papers from Cowles Foundation, Yale University

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 (search for similar items in EconPapers)
JEL-codes: C12 C13 C15 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-rmg
Date: 2002-08

Published in Journal of Econometrics (2006), 133: 673-702

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Journal Article: Higher-order improvements of the parametric bootstrap for long-memory Gaussian processes (2006)
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