No 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.

A new integer-valued autoregressive process (INAR) with Generalised Lagrangian Katz (GLK) innovations is defined. We show that our GLK-INAR process is stationary, discrete semi-self-decomposable, infinite divisible, and provides a flexible modeling framework for count data allowing for under-and overdispersion, asymmetry, and excess of kurtosis. A Bayesian inference framework and an efficient posterior approximation procedure based on Markov Chain Monte Carlo are provided. The proposed model family is applied to a Google Trend dataset which proxies the public concern about climate change around the world. The empirical results provide new evidence of heterogeneity across countries and keywords in the persistence, uncertainty, and long-run public awareness level.