A new INARMA(1, 1) model with Poisson marginals

TL;DR

This paper introduces a novel INARMA(1, 1) model with Poisson marginals, extending INAR(1) similarly to INGARCH(1, 1), and explores its properties and applications through case studies.

Contribution

It proposes a new INARMA(1, 1) model with Poisson marginals, linking it to binomially thinned INAR(1) processes and enabling inference via hidden Markov models.

Findings

Model extends INAR(1) with Poisson marginals

Allows stochastic property analysis and inference methods

Demonstrates effectiveness through case studies

Abstract

We suggest an INARMA(1, 1) model with Poisson marginals which extends the INAR(1) in a similar way as the INGARCH(1, 1) does for the INARCH(1) model. The new model is equivalent to a binomially thinned INAR(1) process. This allows us to obtain some of its stochastic properties and use inference methods for hidden Markov models. The model is compared to various other models in two case studies.