A Periodic Bivariate Integer-Valued Autoregressive Model

In this paper, a bivariate integer-valued autoregressive model with periodic structure is introduced and studied in some detail. The model can be view as a generalization of the one considered in Pedeli and Karlis (Stat. Model. 11:325-349, 2011). Emphasis is placed on models with periodic bivariate Poisson innovations. Basic probabilistic and statistical properties of the model are discussed as well as parameter estimation and forecasting. The proposed model is applied to a bivariate data series concerning the monthly number of fires in neighbor counties, Aveiro and Coimbra, in Portugal.