Parameter change test has been an important issue in time series analysis. The problem has also been actively explored in the field of integer-valued time series, but the testing in the presence of outliers has not yet been extensively investigated. This study considers the problem of testing for parameter change in Poisson autoregressive models particularly when observations are contaminated by outliers. To lessen the impact of outliers on testing procedure, we propose a test based on the density power divergence, which is introduced by Basu et al. (Biometrika 85:549–559, 1998), and derive its limiting null distribution. Monte Carlo simulation results demonstrate validity and strong robustness of the proposed test.

参数更改测试已成为时间序列分析中的重要问题。在整数值时间序列领域中也积极探索了该问题，但是尚未对离群值存在下的测试进行广泛的研究。这项研究考虑了泊松自回归模型中参数变化测试的问题，特别是当观测值受到异常值污染时。为了减少离群值对测试过程的影响，我们提出了一种基于密度幂散度的测试，这是由Basu等人引入的。（Biometrika 85：549-559，1998），并推导其极限零分布。蒙特卡洛仿真结果证明了所提出测试的有效性和强大的鲁棒性。