Some developments on seasonal INAR processes with application to influenza data

Influenza epidemic data are seasonal in nature. Zero-inflation, zero-deflation, overdispersion, and underdispersion are frequently seen in such number of cases of disease (count) data. To explain these counts' features, this paper introduces a flexible model for nonnegative integer-valued time series with a seasonal autoregressive structure. Some probabilistic properties of the model are discussed for general seasonal INAR(p) model and three estimation methods are used to estimate the model parameters for its special case seasonal INAR(1) model. The performance of the estimation procedures has been studied using simulation. The proposed model is applied to analyze weekly influenza data from the Breisgau- Hochschwarzwald county of Baden-Württemberg state, Germany. The empirical findings show that the suggested model performs better than existing models.