A random coefficient integer autoregressive model of order one with seasonal structure (RCINAR(1)s)

Abstract

Seasonality is an inherent part of most of the epidemic data. The fixed coefficient INAR(1) models with seasonal structure have been studied by many authors. The varying immunity and susceptibility affect the chances of catching or escaping an infection. This brings in the randomness in the phenomenon of the spread of the diseases. The fixed coefficient INAR models assume that the chance of infection remains the same for every individual, which is not true practically and hence one needs to study the disease spread phenomenon using random coefficient INAR models. The parameters of the proposed model have been estimated using quasi maximum likelihood estimation. Various probabilistic and inferential properties of the model have been studied. A simulation study has been carried out for parameter estimation. Two data sets having seasonal structures have been analyzed using the model. The model fits well to the data sets compared to the existing models.