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Diagnostic tests before modeling longitudinal actuarial data

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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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    1. Pechon, Florian & Trufin, Julien & Denuit, Michel, 2018. "Multivariate modelling of household claim frequencies in motor third-party liability insurance," LIDAM Reprints ISBA 2018035, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Tzougas, George & Vrontos, Spyridon & Frangos, Nicholas, 2014. "Optimal Bonus-Malus Systems Using Finite Mixture Models," ASTIN Bulletin, Cambridge University Press, vol. 44(2), pages 417-444, May.
    3. Ke Zhu, 2016. "Bootstrapping the portmanteau tests in weak auto-regressive moving average models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 463-485, March.
    4. Lee, Gee Y. & Shi, Peng, 2019. "A dependent frequency–severity approach to modeling longitudinal insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 115-129.
    5. Oh, Rosy & Jeong, Himchan & Ahn, Jae Youn & Valdez, Emiliano A., 2021. "A multi-year microlevel collective risk model," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 309-328.
    6. Pechon, Florian & Trufin, Julien & Denuit, Michel, 2018. "Multivariate Modelling Of Household Claim Frequencies In Motor Third-Party Liability Insurance," ASTIN Bulletin, Cambridge University Press, vol. 48(3), pages 969-993, September.
    7. Antonio Heras & Ignacio Moreno & José L. Vilar-Zanón, 2018. "An application of two-stage quantile regression to insurance ratemaking," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2018(9), pages 753-769, October.
    8. Boucher, Jean-Philippe & Denuit, Michel, 2006. "Fixed versus Random Effects in Poisson Regression Models for Claim Counts: A Case Study with Motor Insurance," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 285-301, May.
    9. Peng Shi & Lu Yang, 2018. "Pair Copula Constructions for Insurance Experience Rating," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 122-133, January.
    10. Lu Yang & Peng Shi, 2019. "Multiperil rate making for property insurance using longitudinal data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 182(2), pages 647-668, February.
    11. Peng Shi & Emiliano Valdez, 2014. "Longitudinal modeling of insurance claim counts using jitters," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2014(2), pages 159-179.
    12. Tzougas, George & Pignatelli di Cerchiara, Alice, 2021. "The multivariate mixed Negative Binomial regression model with an application to insurance a posteriori ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 602-625.
    13. Kang, Seul Ki & Peng, Liang & Xiao, Hongmin, 2020. "Risk analysis with categorical explanatory variables," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 238-243.
    14. Kudryavtsev, Andrey A., 2009. "Using quantile regression for rate-making," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 296-304, October.
    15. Tzougas, George & Vrontos, Spyridon & Frangos, Nicholas, 2014. "Optimal Bonus-Malus Systems using finite mixture models," LSE Research Online Documents on Economics 70919, London School of Economics and Political Science, LSE Library.
    16. Frees, Edward W. & Wang, Ping, 2006. "Copula credibility for aggregate loss models," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 360-373, April.
    17. Edward W. Frees & Gee Lee & Lu Yang, 2016. "Multivariate Frequency-Severity Regression Models in Insurance," Risks, MDPI, vol. 4(1), pages 1-36, February.
    18. Seul Ki Kang & Liang Peng & Andrew Golub, 2021. "Two-step risk analysis in insurance ratemaking," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2021(6), pages 532-542, July.
    19. Jeong, Himchan & Valdez, Emiliano A., 2020. "Predictive compound risk models with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 182-195.
    20. Rosy Oh & Peng Shi & Jae Youn Ahn, 2020. "Bonus-Malus premiums under the dependent frequency-severity modeling," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2020(3), pages 172-195, March.
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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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