Self-exciting hysteretic binomial autoregressive processes

被引:9
作者
Yang, Kai [1 ]
Zhao, Xiuyue [1 ]
Dong, Xiaogang [1 ]
Weiss, Christian H. [2 ]
机构
[1] Changchun Univ Technol, Sch Math & Stat, Changchun, Peoples R China
[2] Helmut Schmidt Univ, Dept Math & Stat, Hamburg, Germany
基金
中国国家自然科学基金;
关键词
Integer-valued time series; Hysteretic autoregressive model; Binomial autoregression; Parameter estimation; RANGE TIME-SERIES; THRESHOLD AUTOREGRESSION; COUNTS; MODELS;
D O I
10.1007/s00362-023-01444-x
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
This paper introduces an observation-driven integer-valued time series model, in which the underlying generating stochastic process is binomially distributed conditional on past information in the form of a hysteretic autoregressive structure. The basic probabilistic and statistical properties of the model are discussed. Conditional least squares, weighted conditional least squares, and maximum likelihood estimators are obtained together with their asymptotic properties. A search algorithm for the two boundary parameters, and the corresponding strong consistency of the estimators, are also provided. Finally, some numerical results on the estimators and a real-data example are presented.
引用
收藏
页码:1197 / 1231
页数:35
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