文章基本信息

标题：Observation-driven models for discrete-valued time series
本地全文：下载
作者：Mirko Armillotta ; Alessandra Luati ; Monia Lupparelli 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2022
卷号：16
期号：1
页码：1393-1433
DOI：10.1214/22-EJS1989
语种：English
出版社：Institute of Mathematical Statistics
摘要：Statistical inference for discrete-valued time series has not been developed like traditional methods for time series generated by continuous random variables. Some relevant models exist, but the lack of a homogenous framework raises some critical issues. For instance, it is not trivial to explore whether models are nested and it is quite arduous to derive stochastic properties which simultaneously hold across different specifications. In this paper, inference for a general class of first order observation-driven models for discrete-valued processes is developed. Stochastic properties such as stationarity and ergodicity are derived under easy-to-check conditions, which can be directly applied to all the models encompassed in the class and for every distribution which satisfies mild moment conditions. Consistency and asymptotic normality of quasi-maximum likelihood estimators are established, with the focus on the exponential family. Finite sample properties and the use of information criteria for model selection are investigated throughout Monte Carlo studies. An empirical application to count data is discussed, concerning a test-bed time series on the spread of an infection.
关键词：62F12;62J12;62M10;62M20;count data;generalized ARMA models;likelihood inference;link-function