The Annals of Statistics

Distribution free goodness-of-fit tests for linear processes

Miguel A. Delgado, Javier Hidalgo, and Carlos Velasco

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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.

Article information

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

First available in Project Euclid: 17 February 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G10: Hypothesis testing 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62F17 62M15: Spectral analysis

Nonparametric model checking spectral distribution linear processes martingale decomposition local alternatives omnibus smooth and directional tests long-range alternatives


Delgado, Miguel A.; Hidalgo, Javier; Velasco, Carlos. Distribution free goodness-of-fit tests for linear processes. Ann. Statist. 33 (2005), no. 6, 2568--2609. doi:10.1214/009053605000000606.

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