Inference and testing for structural change in general Poisson autoregressive models
Inference and testing for structural change in general Poisson autoregressive models
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DOI：
10.1214/15-ejs1038
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发表时间：
2015-01-01
影响因子：
1.1
通讯作者：
Kengne, William
中科院分区：
文献类型：
--
作者：
Doukhan, Paul;Kengne, William
We consider here together the inference questions and the change-point problem in a large class of Poisson autoregressive models (see Tjostheim, 2012 [34]). The conditional mean (or intensity) of the process is involved as a non-linear function of it 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.
