In non-life insurance, it is essential to understand the serial dynamics and dependence structure of the longitudinal insurance data before using them. Existing actuarial literature primarily focuses on modeling, which typically assumes a lack of serial dynamics and a pre-specified dependence structure of claims across multiple years. To fill in the research gap, we develop two diagnostic tests, namely the serial dynamic test and correlation test, to assess the appropriateness of these assumptions and provide justifiable modeling directions. The tests involve the following ingredients: i) computing the change of the cross-sectional estimated parameters under a logistic regression model and the empirical residual correlations of the claim occurrence indicators across time, which serve as the indications to detect serial dynamics; ii) quantifying estimation uncertainty using the randomly weighted bootstrap approach; iii) developing asymptotic theories to construct proper test statistics. The proposed tests are examined by simulated data and applied to two non-life insurance datasets, revealing that the two datasets behave differently.

翻译：在非寿险领域，在使用纵向保险数据之前，理解其序列动态特性和相依结构至关重要。现有精算文献主要侧重于建模，通常假设数据缺乏序列动态特性且各年份索赔具有预设的相依结构。为填补这一研究空白，我们开发了两种诊断性检验——序列动态检验和相关性检验——用于评估这些假设的合理性，并为建模提供可靠的指导方向。这些检验涉及以下要素：i) 计算逻辑回归模型下截面估计参数的变化，以及索赔发生指标随时间变化的经验残差相关性，以此作为检测序列动态特性的指标；ii) 使用随机加权自助法量化估计不确定性；iii) 开发渐近理论以构建适当的检验统计量。通过模拟数据对所提出的检验方法进行验证，并将其应用于两个非寿险数据集，结果表明这两个数据集呈现出不同的特征。