Integer-valued autoregressive processes with dependent counting series are an adaption of INAR processes to dependent counting variables by considering the dependence on the current population via its thinning operator. In this thesis, two classes of classic and threshold INAR(1) processes with introducing a new dependent counting series are proposed. The models provide more features in modeling and analysis of linear and non-linear count time series and are appropriate for modeling the number of dependent random events, which may only produce more new random events or most probably vanish after a period such as the spread of parasitic diseases. Various properties of the process are determined, unknown parameters are estimated by several parametric and non-parametric methods and the behavior of the estimators is described through the numerical results. Also, the models are applied on the real data sets and compared to some relevant INAR(1) models, which confirm the adequacy of the proposed models. The forecasting of the models is provided comprehensively
