A class of count time series models uniting compound Poisson INAR and INGARCH models

Autor:	Bracher, Johannes, Sobolová, Barbora
Rok vydání:	2022
Předmět:	Mathematics - Probability
Druh dokumentu:	Working Paper
Popis:	INAR (integer-valued autoregressive) and INGARCH (integer-valued GARCH) models are among the most commonly employed approaches for count time series modelling, but have been studied in largely distinct strands of literature. In this paper, a new class of generalized integer-valued ARMA (GINARMA) models is introduced which unifies a large number of compound Poisson INAR and INGARCH processes. Its stochastic properties, including stationarity and geometric ergodicity, are studied. Particular attention is given to a generalization of the INAR($p$) model which parallels the extension of the INARCH(p) to the INGARCH(p, q) model. For inference, we consider moment-based estimation and a maximum likelihood inference scheme inspired by the forward algorithm. Models from the proposed class have a natural interpretation as stochastic epidemic processes, which throughout the article is used to illustrate our arguments. In a case study, different instances of the class, including both established and newly introduced models, are applied to weekly case numbers of measles and mumps in Bavaria, Germany. Comment: 22 pages, 3 figures, 2 tables (main text)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2204.12449 Zobrazit plný text záznamu View this record from Arxiv