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Estimation and testing linearity for non-linear mixed Poisson autoregressions. (English) Zbl 1327.62456

Summary: Non-linear mixed Poisson autoregressive models are studied for the analysis of count time series. Given a correct mean specification of the model, we discuss quasi maximum likelihood estimation based on Poisson log-likelihood function. A score testing procedure for checking linearity of the mean process is developed. We consider the cases of identifiable and non identifiable parameters under the null hypothesis. When the parameters are identifiable then a chi-square approximation to the distribution of the score test is obtained. In the case of non identifiable parameters, a supremum score type test statistic is employed for checking linearity of the mean process. The methodology is applied to simulated and real data.

MSC:

62M09 Non-Markovian processes: estimation
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)

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