An integer-valued AR(1) process with Poisson-modified Lindley distributed innovation and modelling practical time series data

An integer-valued AR(1) process with Poisson-modified Lindley distributed innovation

Abstract

In this paper, a first-order, non-negative, integer-valued autoregressive model with Poisson-modified Lindley distributed innovation is developed. In contrast to the standard Poisson distribution, modern models can accommodate count time series data with over-dispersion. Statistical properties of the proposed model, including the mean, variance, conditional mean, conditional variance, and multi-step forecast conditional measures, are studied. To estimate the parameter of the model, conditional maximum likelihood estimation is used. The model's utility is demonstrated using two real-world data sets: the number of times a software is downloaded and the number of sudden death submissions of animals at a hospital in New Zealand.