Inference and testing for structural change in general Poisson autoregressive models.(English)Zbl 1349.62397

Summary: We consider here together the inference questions and the change-point problem in a large class of Poisson autoregressive models (see [D. Tjøstheim, Test 21, No. 3, 413–438 (2012; Zbl 1362.62174)]). The conditional mean (or intensity) of the process is involved as a non-linear function of its past values and the past observations. Under Lipschitz-type conditions, it can be written as a function of lagged observations. For the latter model, assume that the link function depends on an unknown parameter $$\theta_{0}$$. The consistency and the asymptotic normality of the maximum likelihood estimator of the parameter are proved. These results are used to study change-point problem in the parameter $$\theta_{0}$$. From the likelihood of the observations, two tests are proposed. Under the null hypothesis (i.e. no change), each of these tests statistics converges to an explicit distribution. Consistencies under alternatives are proved for both tests. Simulation results show how those procedures work in practice, and applications to real data are also processed.

MSC:

 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62F12 Asymptotic properties of parametric estimators 62F10 Point estimation 62F03 Parametric hypothesis testing 62F05 Asymptotic properties of parametric tests 65C60 Computational problems in statistics (MSC2010) 60F05 Central limit and other weak theorems

Zbl 1362.62174
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References:

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