An INAR model with discrete Laplace marginal distributions

In this paper, we first introduce a new thinning operator and derive some of its properties. Then, by using the thinning operator we define a new stationary time series with discrete Laplace marginal distributions with either positive or negative lag-one autocorrelation. We show that this time series is distributed as the difference of two independent NGINAR (1) time series and, using this fact, we discuss some of its properties. The Yule–Walker estimators for the unknown parameters are derived and their asymptotic properties are discussed.