Abstract After having fitted a model to a given count time series, one has to check the adequacy of this model fit. The (standardized) Pearson residuals, being easy to compute and interpret, are a popular diagnostic approach for this purpose. But which types of model inadequacy might be uncovered by which statistics based on the Pearson residuals? In view of being able to apply such statistics in practice, it is also crucial to ask for the properties of these statistics under model adequacy. We look for answers to these questions by means of a comprehensive simulation study, which considers diverse types of count time series models and inadequacy scenarios. We illustrate our findings with two real-data examples about strikes in the U.S., and about corporate insolvencies in the districts of Rhineland–Palatinate. We conclude with a theoretical discussion of Pearson residuals.

中文翻译：

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使用Pearson残差检查计数时间序列的模型充分性

摘要在将模型拟合到给定的计数时间序列后，必须检查该模型拟合的充分性。易于计算和解释的（标准化）皮尔逊残差是用于此目的的流行诊断方法。但是，哪些基于Pearson残差的统计数据可能会发现哪些类型的模型不足？鉴于能够在实践中应用此类统计信息，在模型适当性下要求这些统计信息的属性也至关重要。我们通过全面的模拟研究来寻找这些问题的答案，该研究考虑了各种类型的计数时间序列模型和不足的情况。我们用两个关于美国罢工以及莱茵兰-普法尔茨州企业破产的真实数据示例来说明我们的发现。