Journal Article

Self-Excited Threshold Poisson Autoregression

Davis, Richard A, Yao, Jian-Feng, Wang, Chao, Liu, Heng, Li, Wai Keung

2014

Overview

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.

• Publisher: Taylor & Francis,Taylor & Francis Group, LLC,Taylor & Francis Ltd
• Subject: Autocorrelation / Earthquakes / Estimators / Inference / Integer-valued GARCH / Invariant probability measure / Law of large numbers / Markov analysis / Markov chain / Markov chains / Maximum likelihood estimation / Maximum likelihood estimators / Natural disasters / Poisson distribution / Probability / Regression analysis / Sample size / Self-excited threshold process / Simulation / Simulations / Statistics / Strong law of large numbers / Theory / Theory and Methods / Time series / time series analysis / Time series models / Time series of counts