Open Access
2015 Inference and testing for structural change in general Poisson autoregressive models
Paul Doukhan, William Kengne
Electron. J. Statist. 9(1): 1267-1314 (2015). DOI: 10.1214/15-EJS1038


We consider here together the inference questions and the change-point problem in a large class of Poisson autoregressive models (see Tjøstheim, 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.


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Paul Doukhan. William Kengne. "Inference and testing for structural change in general Poisson autoregressive models." Electron. J. Statist. 9 (1) 1267 - 1314, 2015.


Received: 1 February 2015; Published: 2015
First available in Project Euclid: 19 June 2015

zbMATH: 1349.62397
MathSciNet: MR3358325
Digital Object Identifier: 10.1214/15-EJS1038

Primary: 60G10 , 62F12 , 62M10
Secondary: 62F03 , 62F05 , 62F10

Keywords: Change-point , Likelihood estimation , Poisson autoregression , semi-parametric test , time series of counts

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.9 • No. 1 • 2015
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