Time series in real-world applications often have missing observations, making typical analytical methods unsuitable. One method for dealing with missing data is the concept of amplitude modulation. While this principle works with any data, here, missing data for unbounded and bounded count time series are investigated, where tailor-made dispersion and skewness statistics are used for model diagnostics. General closed-form asymptotic formulas are derived for such statistics with only weak assumptions on the underlying process. Moreover, closed-form formulas are derived for the popular special cases of Poisson and binomial autoregressive processes, always under the assumption that missingness occurs. The finite-sample performances of the considered asymptotic approximations are analyzed with simulations. The practical application of the corresponding dispersion and skewness tests under missing data is demonstrated with three real-data examples.

翻译：现实世界的时间序列常存在观测缺失，这使得常规分析方法不再适用。处理缺失数据的一种方法是振幅调制原理。虽然该原理适用于任何数据类型，但本文针对无界和有界计数时间序列中的缺失数据展开研究，采用特制的离散度和偏度统计量进行模型诊断。在仅对基础过程作弱假设的条件下，推导了此类统计量的通用闭式渐近公式。进一步地，在始终假设存在缺失性的前提下，推导了泊松和二项自回归过程这两种常见特例的闭式公式。通过仿真分析了所考虑渐近近似方法的有限样本表现，并利用三个真实数据实例展示了缺失数据下相应离散度与偏度检验的实际应用。