Electronic Journal of Statistics

Estimation and testing linearity for non-linear mixed poisson autoregressions

Vasiliki Christou and Konstantinos Fokianos

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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

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

Received: January 2015
First available in Project Euclid: 23 June 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62M09: Non-Markovian processes: estimation
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Bootstrap chi-square contraction identifiability quasi maximum likelihood score test threshold model


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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