The INMA(1) model, an integer-valued counterpart to the usual moving-average model of order 1, gained recently importance for insurance applications. After a comprehensive discussion of stochastic properties of the INMA(1) model, we develop diagnostic tests regarding the marginal distribution (overdispersion, zero inflation) and the autocorrelation structure. We also derive formulae for correcting the bias of point estimators and for constructing joint confidence regions. These inferential approaches rely on asymptotic properties, the finite-sample performance of which is investigated with simulations. A real-data example illustrates the application of the novel diagnostic tools.

中文翻译：

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INMA（1）过程的参数估计和诊断测试

INMA（1）模型是通常的1阶移动平均模型的整数对应模型，最近在保险应用中变得越来越重要。在对INMA（1）模型的随机属性进行全面讨论之后，我们开发了有关边际分布（过度分散，零膨胀）和自相关结构的诊断测试。我们还导出了用于校正点估计量的偏差并构造联合置信区域的公式。这些推论方法依赖于渐近性质，并通过仿真研究了其有限样本性能。实际数据示例说明了新型诊断工具的应用。