Self-Excited Threshold Poisson Autoregression

By Chao Wang, Heng Liu, Jianfeng Yao, Richard A. Davis, Wai Keung Li. 2013

109 citations recorded by the source corpus.

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.

Subfields: Environmental Engineering, Finance, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/7a74a6c68c1248571f1803d576f5df6623ab3e69

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Environmental Engineering

1. Richard A. Davis
2. Harry Joe
3. Scott H. Holan
4. Ciprian A. Tudor

In Finance

1. Konstantinos Fokianos
2. Richard A. Davis
3. Harry Joe
4. Heng Liu
5. Vladas Pipiras
6. Robert B. Lund
7. Scott H. Holan
8. Claudia Czado

In Global and Planetary Change

1. Richard A. Davis
2. Harry Joe
3. Xiaolan L. Wang

Citations in the corpus

• Count Time Series: A Methodological Review (2021, methodology): “Other nonlinear models for count time series analysis have been studied in Fokianos and Tjøstheim (2012), Christou and Fokianos (2014), and Wang et al. (2014).”
• Theory and inference for a class of nonlinear models with application to time series of counts (2016, methodology): “Wang et al. (2014) proposed the self-excited threshold Poisson autoregression model as a generalization to the Poisson INGARCH (4.5) is an attempt to model negative autocorrelation.”