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Diagnostic tests before modeling longitudinal actuarial data

Author

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  • Li, Yinhuan
  • Fung, Tsz Chai
  • Peng, Liang
  • Qian, Linyi

Abstract

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.

Suggested Citation

  • Li, Yinhuan & Fung, Tsz Chai & Peng, Liang & Qian, Linyi, 2023. "Diagnostic tests before modeling longitudinal actuarial data," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 310-325.
    • Handle: RePEc:eee:insuma:v:113:y:2023:i:c:p:310-325
    DOI: 10.1016/j.insmatheco.2023.09.002
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    More about this item

    Keywords

    Insurance loss; Claim occurrence probability; Logistic regression; Longitudinal data; Random weighted bootstrap;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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