First-order integer-valued auto-regressive process with discrete Lindley distribution marginal

In this paper, we propose a stationary first-order integer-valued auto-regressive (INAR(1)) process with the DLD marginal distribution (DLD-INAR(1)) for dealing with overdispersed data. Several statistical properties of the model are established, such as conditional measures, autocorrelation, and non-reversibility over time. We consider the conditional maximum likelihood method to estimate the model's unknown parameters and study the properties of the estimators. The model is applied to a real-world time series dataset to evaluate its competitiveness against other INAR(1) models.