Analysis of first-order integer-valued autoregressive models

The Poisson distribution is often used for the distribution of errors in integer-valued autoregressive models. However, the mean of the distribution is equal to its variance and is suitable for equally distributed series. Real integer-valued time series are often over- or under-dispersion. Therefore, many first-order integer-valued autoregressive (INAR(1)) models based on binomial thinning with differently distributed errors have been developed in the literature. In this thesis, INAR(1) models in the literature for modeling integer-valued time series are examined in detail. The models are compared with certain criteria on two different real integer-valued time series, one of which is overdispersion and the other is underdispersion, and the most appropriate INAR(1) models are determined for the series.