A combined DLD-INAR(p) model for overdispersed count data

In this paper, we develop a combined order p integer-valued autoregressive process whose marginal distribution follows the discrete Lindley distribution (DLD) [1]. Referred to as the CDLD-INAR(p) process, this model is particularly suited for modeling count time series exhibiting overdispersion. Formulation of this model is based on the binomial thinning operator introduced by Steutel [8]. Several conditional theoretical properties of the process are established, and its parameters are estimated using the conditional maximum likelihood method. The asymptotic properties of the resulting estimators are also investigated. Finally, the practical relevance of the proposed model is demonstrated through an application to real data.