Self-Excited Threshold Poisson Autoregression

• 成果类型: Article
• 署名作者: Wang, Chao; Liu, Heng; Yao, Jian-feng; Davis, Richard A.; Li, Wai Keung
• 署名单位: University of Hong Kong; Alphabet Inc.; Google Incorporated; Columbia University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2013.872994
• 发表日期: 2014
• 页码: 777-787
• 关键词: iterated random functions; time-series; models; ergodicity; GARCH

摘要

This article studies theory and inference of an observation-driven model for time series of counts. It is assumed that the observations follow a Poisson distribution conditioned on an accompanying intensity process, which is equipped with a two-regime structure according to the magnitude of the lagged observations. Generalized from the Poisson autoregression, it allows more flexible, and even negative correlation, in the observations, which cannot be produced by the single-regime model. Classical Markov chain theory and Lyapunov's method are used to derive the conditions under which the process has a unique invariant probability measure and to show a strong law of large numbers of the intensity process. Moreover, the asymptotic theory of the maximum likelihood estimates of the parameters is established. A simulation study and a real-data application are considered, where the model is applied to the number of major earthquakes in the world. Supplementary materials for this article are available online.