This paper presents a new stationary integer-valued bilinear time series model of the first order by mixing the thinning and Pegram operators. Some statistical properties of the model are obtained, involving the conditional moments, autocovariance and spectral density function. Estimation of the model parameters is discussed using the Yule-Walker and conditional least squares methods with a simulation study for evaluating the performance of those estimators. Applicability of the process is investigated using a practical count data set with comparing the model to a competitive bilinear model using some marginal distributions of innovations. Issue of forecasting data is discussed under the proposed model.
