Distribution free goodness-of-fit tests for linear processes

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

2006-03-02

arxiv.org/abs/math/0603043v1

Annals of Statistics 2005, Vol. 33, No. 6, 2568-2609

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053605000000606 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

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 $T_p$-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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