To provide a more flexible model of count data, we extend the first-order integer-valued autoregressive model with serially dependent innovations based on the dependent thinning operator. This model is appropriate for modelling the number of dependent random events affecting each other when the number of new cases depend on the previous count through a linear functional relationship. Several statistical properties of the model are determined, parameters are estimated by some methods and their properties are studied via simulations. This study was carried out to investigate the efficiency of the new model by two real count data sets, the number of contagious diseases and robbery.
