In this study, we consider a robust estimation method for general integer-valued time series models whose conditional distribution belongs to the one-parameter exponential family. As a robust estimator, we employ the minimum density power divergence estimator, and we demonstrate this is strongly consistent and asymptotically normal under certain regularity conditions. A simulation study is carried out to evaluate the performance of the proposed estimator. A real data analysis using the return times of extreme events of the Goldman Sachs Group stock is also provided as an illustration.

中文翻译：

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一般整数值时间序列模型的稳健估计

在这项研究中，我们考虑了一种适用于条件分布属于单参数指数族的一般整数值时间序列模型的稳健估计方法。作为一个稳健的估计器，我们使用了最小密度功率散度估计器，并且我们证明了在某些规律性条件下这是强一致性和渐近正态的。进行模拟研究以评估所提出的估计器的性能。还提供了使用高盛集团股票极端事件重现时间的真实数据分析作为说明。