The present work proposes a new INAR(1) model based on the Pegram and thinning operators, where the innovations are supposed to be serially dependent to the current population. Several properties of the model are discussed. Maximum likelihood and modified Yule-Walker methods besides, a new sieve bootstrap approach are considered for the parameter estimation of the model and their performances and forecasting methods are checked by a simulation. This survey was carried out to study the efficiency of the new model by applying it on a real data.
