In this study, we consider the problem of testing for a parameter change in general integer-valued time series models whose conditional distribution belongs to the one-parameter exponential family when the data are contaminated by outliers. In particular, we use a robust change point test based on density power divergence (DPD) as the objective function of the minimum density power divergence estimator (MDPDE). The results show that under regularity conditions, the limiting null distribution of the DPD-based test is a function of a Brownian bridge. Monte Carlo simulations are conducted to evaluate the performance of the proposed test and show that the test inherits the robust properties of the MDPDE and DPD. Lastly, we demonstrate the proposed test using a real data analysis of the return times of extreme events related to Goldman Sachs Group stock.
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机译：在这项研究中，我们考虑当数据被异常值污染时，其条件分布所属的一般整数值时间序列模型中的参数变化的测试问题。特别地，我们使用基于密度功率发散（DPD）作为最小密度功率发散估计器（MDPDE）的目标函数来使用鲁棒的改变点测试。结果表明，在规律条件下，基于DPD的测试的限制空分布是布朗桥的函数。 Monte Carlo仿真进行了评估所提出的测试的性能，并表明测试继承了MDPDE和DPD的强大属性。最后，我们展示了使用与Goldman Sachs Group Stock相关的极端事件的返回时间的真实数据分析来证明所提出的测试。
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