Time series count data exhibit varying dispersion due to their sparse nature. Given the assumption on the incident rate structure, the methodology that can adequately accommodate the dispersion and inflation characteristics of count data is investigated. We develop Poisson distribution based autoregressive models that can account for dispersion and zero inflation indices in count series data. We derive the maximum likelihood estimators of the parameters in the models developed. The dispersion indices for these models depend on the structure of the incidence rate specified.

count data, dispersion, inflation index, Poisson distribution, autoregressive model.