Generalized Poisson integer-valued autoregressive processes with structural changes

Abstract

In this paper, we introduce a new first-order generalized Poisson integer-valued autoregressive process, for modeling integer-valued time series exhibiting a piecewise structure and overdispersion. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares and conditional maximum likelihood estimators are derived. The asymptotic properties of the estimators are established. Moreover, two special cases of the process are discussed. Finally, some numerical results of the estimates and a real data example are presented.

Keywords:

• Structural changes INAR models
• generalized poisson distribution
• binomial thinning
• moments targeting estimation
• non-stationary process

Acknowledgments

We gratefully acknowledge the anonymous reviewers for their careful work and thoughtful suggestions that have helped improve this article substantially.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 We know that the ADF test is an unit root test for the AR time series models. However, we can verify that SETGPINAR(1) model (15(15) $X_t=\{\begin{array}{ll}{\alpha }_1\circ X_{t-1}+{\epsilon }_t,& X_{t-1}\le r,\\ {\alpha }_2\circ X_{t-1}+{\epsilon }_t,& X_{t-1}>r,\end{array}t\in \mathbb{Z}.$(15) ) is a first-order GPINAR model. As discussed by Latour (1998) that, the GPINAR(p) process is nothing but an AR(p) process. Thereby, the ADF is applicable here.

Additional information

Funding

This work is supported by National Natural Science Foundation of China [No. 11731015,11871028,11901053,12001229], Natural Science Foundation of Jilin Province [No. 20180101216JC], Program for Changbaishan Scholars of Jilin Province [2015010].