A note on an integer valued time series model with Poisson-negative binomial marginal distribution

摘要

This paper proposes a new model for autoregressive time series of counts in terms of a convolution of Poisson and negative binomial random variables, known as Poisson-negative binomial (PNB) distribution. The corresponding first-order integer valued time series models are developed and their properties are discussed. The geometric PNB and the geometric semi PNB distributions are also introduced and studied.