Integer-valued autoregressive processes with periodic structure

In this paper the periodic integer-valued autoregressive model of order one with period T, driven by a periodic sequence of independent Poisson-distributed random variables, is studied in some detail. Basic probabilistic and statistical properties of this model are discussed. Moreover, parameter estimation is also addressed. Specifically, the methods of estimation under analysis are the method of moments, least squares-type and likelihood-based ones. Their performance is compared through a simulation study.