Distribution free goodness-of-fit tests for linear processes
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The Annals of Statistics

Distribution free goodness-of-fit tests for linear processes

Miguel A. Delgado, Javier Hidalgo, and Carlos Velasco

Source: Ann. Statist. Volume 33, Number 6 (2005), 2568-2609.

Abstract

This article proposes a class of goodness-of-fit tests for the autocorrelation function of a time series process, including those exhibiting long-range dependence. Test statistics for composite hypotheses are functionals of a (approximated) martingale transformation of the Bartlett Tp-process with estimated parameters, which converges in distribution to the standard Brownian motion under the null hypothesis. We discuss tests of different natures such as omnibus, directional and Portmanteau-type tests. A Monte Carlo study illustrates the performance of the different tests in practice.

Primary Subjects: 62G10, 62M10
Secondary Subjects: 62F17, 62M15
Keywords: Nonparametric model checking; spectral distribution; linear processes; martingale decomposition; local alternatives; omnibus; smooth and directional tests; long-range alternatives

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aos/1140191667
Digital Object Identifier: doi:10.1214/009053605000000606
Mathematical Reviews number (MathSciNet): MR2253096
Zentralblatt MATH identifier: 1084.62038

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