Review and Application of Two Integer - Valued Time Series Models

This paper first introduces Delaporte and first type Luders Formel models. Then these models are considered as stationary marginal distributions for first-order integer – valued autoregressive processes. After that, the higher order integer - valued autoregressive processes are considered. Various features of these models such as regressive behavior, time reversible and etc. are studied. Also Simulation studies for study of sample paths in these models were done. Finally, the model parameters were estimated and the two models are compared via a real data set.