Pearson residuals are a widely used tool for model diagnostics of count time series. Despite their popularity, little is known about their distribution such that statistical inference is problematic. Squared Pearson residuals are considered for testing the conditional dispersion structure of the given count time series. For two popular types of Markov count processes, an asymptotic approximation for the distribution of the test statistics is derived. The performance of the novel tests is analyzed and compared to relevant competitors. Illustrative data examples are presented, and possible extensions of our approach are discussed.

中文翻译：

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使用Pearson残差测试计数时间序列的离散结构

皮尔逊残差是用于计数时间序列模型诊断的广泛使用的工具。尽管它们很受欢迎，但对其分布却知之甚少，因此统计推断存在问题。考虑平方的皮尔逊残差以测试给定计数时间序列的条件色散结构。对于两种流行的马尔可夫计数过程类型，得出了检验统计量分布的渐近近似。分析新颖测试的性能，并将其与相关竞争对手进行比较。给出了说明性的数据示例，并讨论了我们方法的可能扩展。