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Testing for a linear MA model against threshold MA models. (English) Zbl 1085.62102

Summary: This paper investigates the (conditional) quasi-likelihood ratio test for the threshold in moving average (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.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
60F05 Central limit and other weak theorems
62F05 Asymptotic properties of parametric tests
62M07 Non-Markovian processes: hypothesis testing
60G10 Stationary stochastic processes
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