Self-excited threshold Poisson autoregressive model with covariables

Xinyang Wang, Danshu Sheng and Tengyue Ma

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 17, 5406-5427

Abstract: This article introduces a self-excited threshold Poisson autoregressive model with covariables. The framework of our model possesses sufficient capability to accurately capture the characteristics of count time series, including temporal volatility changes, clusters with high threshold exceedances, and the so-called piecewise phenomenon. The stationarity and moment existence of the model are discussed. The conditional maximum likelihood estimator of parameters is derived, and we establish their asymptotic properties. Additionally, this study addresses the non linearity test and covariables existence test for the model. Finally, our methodology is validated through some simulations and a real data analysis.

Date: 2025
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DOI: 10.1080/03610926.2024.2437500

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