  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.
