Electronic Journal of Statistics

Inference and testing for structural change in general Poisson autoregressive models

Paul Doukhan and William Kengne

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Statist. Volume 9, Number 1 (2015), 1267-1314.

Dates
Received: February 2015
First available in Project Euclid: 19 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1434720539

Digital Object Identifier
doi:10.1214/15-EJS1038

Mathematical Reviews number (MathSciNet)
MR3358325

Zentralblatt MATH identifier
1349.62397

Subjects
Primary: 60G10: Stationary processes 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62F12: Asymptotic properties of estimators
Secondary: 62F03: Hypothesis testing 62F05: Asymptotic properties of tests 62F10: Point estimation

Keywords
Time series of counts Poisson autoregression likelihood estimation change-point semi-parametric test

Citation

Doukhan, Paul; Kengne, William. Inference and testing for structural change in general Poisson autoregressive models. Electron. J. Statist. 9 (2015), no. 1, 1267--1314. doi:10.1214/15-EJS1038. https://projecteuclid.org/euclid.ejs/1434720539.


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