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Distribution free goodness-of-fit tests for linear processes

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URI: https://hdl.handle.net/10016/2491
ISSN: 0090-5364
DOI: 10.1214/009053605000000606
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DELGADO_TAS_2005_33_6_DM.pdf (417.88 KB)
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2005
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Institute of Mathematical Statistics
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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.
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Nonparametric model checking, Spectral distribution, Linear processes, Martingale decomposition, Local alternatives, Omnibus, Smooth and directional tests, Long range alternatives
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Annals of Statistics, 2005, vol. 33, nº 6, p. 2568-2609
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