Generalized Poisson Difference Autoregressive Processes

Abstract

This paper introduces a new stochastic process with values in the set Z of integers with sign. The increments of process are Poisson differences and the dynamics has an autoregressive structure. We study the properties of the process and exploit the thinning representation to derive stationarity conditions and the stationary distribution of the process. We provide a Bayesian inference method and an efficient posterior approximation procedure based on Monte Carlo. Numerical illustrations on both simulated and real data show the effectiveness of the proposed inference.

Models for Integer Data

“…GP denotes the generalized Poisson distribution. Carallo et al (2020) proposed a model based on the GPD distribution. For λ = 0, the two distributions are simple Poisson, and we get the Skellam.…”