## The Annals of Statistics

### Distribution free goodness-of-fit tests for linear processes

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 17 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.aos/1140191667

Digital Object Identifier
doi:10.1214/009053605000000606

Mathematical Reviews number (MathSciNet)
MR2253096

Zentralblatt MATH identifier
1084.62038

#### Citation

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. https://projecteuclid.org/euclid.aos/1140191667

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