The paper focuses on a new stationary integer-valued autoregressive model of first order with Poisson-Lindley marginal distribution. Several statistical properties of the model are established, like spectral density function, multi-step ahead conditional measures, stationarity, ergodicity and irreducibility. We consider several methods for estimating the unknown parameters of the model and investigate properties of the estimators. The performances of these estimators are compared via simulation. The model is motivated by some applications to two real count time series data.
