First-order integer-valued autoregressive processes with Generalized Katz innovations

TL;DR

This paper introduces a flexible new integer-valued autoregressive model with generalized innovations, capable of capturing complex features in count data, and applies it to analyze global climate change concern trends.

Contribution

It develops a novel INAR model with Generalized Lagrangian Katz innovations, including theoretical properties, extensions, and a Bayesian inference framework.

Findings

Model captures heterogeneity in climate concern data

Provides insights into persistence and uncertainty in public awareness

Demonstrates model's applicability to real-world time series

Abstract

A new integer--valued autoregressive process (INAR) with Generalised Lagrangian Katz (GLK) innovations is defined. This process family provides a flexible modelling framework for count data, allowing for under and over--dispersion, asymmetry, and excess of kurtosis and includes standard INAR models such as Generalized Poisson and Negative Binomial as special cases. We show that the GLK--INAR process is discrete semi--self--decomposable, infinite divisible, stable by aggregation and provides stationarity conditions. Some extensions are discussed, such as the Markov--Switching and the zero--inflated GLK--INARs. A Bayesian inference framework and an efficient posterior approximation procedure are introduced. The proposed models are applied to 130 time series from Google Trend, which proxy the worldwide public concern about climate change. New evidence is found of heterogeneity across time, countries and keywords in the persistence, uncertainty, and long--run public awareness level.