Work

Inference and testing for structural change in general Poisson autoregressive models

Year: 2015

Type: article

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.

Source: Electronic Journal of Statistics

DOI: 10.1214/15-ejs1038

Authors: Paul Doukhan, William Kengne

Institutions: Analyse, Géométrie et Modélisation, Théorie Économique, Modélisation et Applications

Language: English

Topic: Advanced Statistical Process Monitoring

Subfield: Statistics, Probability and Uncertainty

Field: Decision Sciences

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $675

Funder: Agence Nationale de la Recherche