The modeling and analysis of count time series have developed extensively by taking into account the different features of the data. A variety of thinning operators and various integer-valued models have been introduced regarding the various characteristics of the data. In this thesis, a new discrete distribution is studied which has the following features: overdispersed, underdispersed, zero-inflated and zero-deflated. An INAR(1) model is defined based on the counting variables. The model parameters are estimated and tried to examine the estimators with a simulation study. Using two real data, the proposed model is compared with three traditional models and the model gives the most satisfactory results among the alternative models based on the variance and index dispersion.
