Testing for a linear MA model against threshold MA models

Details Testing for a linear MA model against threshold MA models Testing for a linear MA model against threshold MA models

2006-03-02

arxiv.org/abs/math/0603040v1

Annals of Statistics 2005, Vol. 33, No. 6, 2529-2552

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053605000000598 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053605000000598

This paper investigates the (conditional) quasi-likelihood ratio test for the threshold in MA models. Under the hypothesis of no threshold, it is shown that the test statistic converges weakly to a function of the centred Gaussian process. Under local alternatives, it is shown that this test has nontrivial asymptotic power. The results are based on a new weak convergence of a linear marked empirical process, which is independently of interest. This paper also gives an invertible expansion of the threshold MA models.

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