期刊
ELECTRONIC JOURNAL OF STATISTICS
卷 16, 期 1, 页码 1393-1433出版社
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/22-EJS1989
关键词
Count data; generalized ARMA models; likelihood inference; link-function
资金
- European Regional Development Fund
- Republic of Cyprus through the Research and Innovation Foundation [INFRASTRUCTURES/1216/0017]
This paper develops inference for a general class of first order observation-driven models for discrete-valued processes. Stochastic properties are derived under easy-to-check conditions, and consistency and asymptotic normality of quasi-maximum likelihood estimators are established.
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.
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