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December 2005 Distribution free goodness-of-fit tests for linear processes
Miguel A. Delgado, Javier Hidalgo, Carlos Velasco
Ann. Statist. 33(6): 2568-2609 (December 2005). DOI: 10.1214/009053605000000606


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.


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Miguel A. Delgado. Javier Hidalgo. Carlos Velasco. "Distribution free goodness-of-fit tests for linear processes." Ann. Statist. 33 (6) 2568 - 2609, December 2005.


Published: December 2005
First available in Project Euclid: 17 February 2006

zbMATH: 1084.62038
MathSciNet: MR2253096
Digital Object Identifier: 10.1214/009053605000000606

Primary: 62G10 , 62M10
Secondary: 62F17 , 62M15

Keywords: linear processes , local alternatives , long-range alternatives , martingale decomposition , Nonparametric model checking , omnibus , smooth and directional tests , Spectral distribution

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 6 • December 2005
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