Abstract:
Analysing autoregressive counts over time remains a relevant and evolving matter of
interest, where oftentimes the assumption of normality is made for the error terms. In the case
when data are discrete, the Poisson model may be assumed for the structure of the error terms.
In order to address the equidispersion restriction of the Poisson distribution, various alternative
considerations have been investigated in such an integer environment. This paper, inspired by
the integer autoregressive process of order 1, incorporates negative binomial shape mixtures via a
compound Poisson Lindley model for the error terms. The systematic construction of this model is
offered and motivated, and is analysed comparatively against common alternate candidates with a
number of simulation and data analyses. This work provides insight into noncentral-type behaviour
in both the continuous Lindley model and in the discrete case for meaningful application and
consideration in integer autoregressive environments.
