Serial dependence and regression of Poisson INARMA models

Time series of counts occur in many fields of practice, with the Poisson distribution as a popular choice for the marginal process distribution. A great variety of serial dependence structures of stationary count processes can be modelled by the INARMA family. In this article, we propose a new approach to the INMA(q) family in general, including previously known results as special cases. In the particular case of Poisson marginals, we will derive new results concerning regression properties and the serial dependence structure of INAR(1) and INMA(q) models. Finally, we present explicit expressions for the distribution of jumps in such processes.