Self-exciting threshold models for time series of counts with a finite range

Abstract

In this article, an integer-valued self-exciting threshold model with a finite range based on the binomial INARCH(1) model is proposed. Important stochastic properties are derived, and approaches for parameter estimation are discussed. A real-data example about the regional spread of public drunkenness in Pittsburgh demonstrates the applicability of the new model in comparison to existing models. Feasible modifications of the model are presented, which are designed to handle special features such as zero-inflation.

Keywords:

• Binomial INARCH(1) model
• count data time series
• parameter estimation
• self-exciting threshold
• zero-inflation

Mathematics Subject Classification:

• 60J10
• 62M05
• 62M10

Acknowledgment

The author thanks the editor and the referee for carefully reading the paper and for their comments, which greatly improved the article. He is also grateful to Christian H. Weiß for the useful comments and help in improving this article.