An INAR(1) model with Poisson-Lindley innovations

Real count data time series often show the phenomenon of the overdispersion. In this paper, we introduce a first order non-negative integer valued autoregressive process with Poisson-Lindley innovations based on the binomial thinning operator. The new model is particularly suitable for time series of counts exhibiting overdispersion and therefore competes against others recently established. The main properties of the model are derived. The methods of conditional least squares, Yule-Walker and conditional maximum likelihood are used for estimating the parameters. The proposed model is also applied to a weekly sales of soap product data series.