## Electronic Journal of Statistics

### Estimation and testing linearity for non-linear mixed poisson autoregressions

#### Abstract

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.

#### Article information

Source
Electron. J. Statist., Volume 9, Number 1 (2015), 1357-1377.

Dates
First available in Project Euclid: 23 June 2015

https://projecteuclid.org/euclid.ejs/1435064563

Digital Object Identifier
doi:10.1214/15-EJS1044

Mathematical Reviews number (MathSciNet)
MR3360730

Zentralblatt MATH identifier
1327.62456

#### Citation

Christou, Vasiliki; Fokianos, Konstantinos. Estimation and testing linearity for non-linear mixed poisson autoregressions. Electron. J. Statist. 9 (2015), no. 1, 1357--1377. doi:10.1214/15-EJS1044. https://projecteuclid.org/euclid.ejs/1435064563

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