A New INARMA(1, 1) Model with Poisson Marginals

Abstract

We suggest a new 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 proposed 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. We conduct a simulation study and compare the model to various other models from the literature in two case studies.