  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.
