In this paper, we introduce a new stationary integer-valued autoregressive process of the first order with geometric marginal based on mixing Pegram and generalized binomial thinning operators. The count series of the process consists of dependent Bernoulli count variables. Various properties of the process are obtained, including the distribution of its innovation process. Maximum likelihood estimation by EM algorithm is applied to estimate the parameters of the process and the performance of the estimates is checked by Monte Carlo simulation. We investigate applicability of the process using a real count data set and compare the process to many competitive INAR(1) models via some goodness-of-fit statistics. As a result, forecasting of the data is discussed under the proposed process.
