An INAR model with discrete Laplace marginal distributions

Abstract

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 $\operatorname{NGINAR} (1)$ 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.