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An observation-driven state-space count model for experience rating

Author

Listed:
  • Ahn, Jae Youn
  • Jeong, Himchan
  • Lu, Yang
  • Wüthrich, Mario V.

Abstract

State-space models are widely used in applications, e.g., in economics, finance and actuarial science. In the domain of count data, one such example is the model proposed by Harvey and Fernandes (1989). Unlike many of its parameter-driven alternatives, this model is observation-driven, and it leads to a closed-form expression for the predictive density. This predictive density takes into account past observations by assigning a seniority weighting to them. This feature makes this model very appealing for general insurance ratemaking. However, the model of Harvey and Fernandes (1989) has the property that the variance diverges in the long-run, which might be an undesirable model feature. In this paper, we extend the model of Harvey and Fernandes (1989) by allowing for flexible variance specifications including non-explosive ones, while keeping the model fully tractable.

Suggested Citation

  • Ahn, Jae Youn & Jeong, Himchan & Lu, Yang & Wüthrich, Mario V., 2025. "An observation-driven state-space count model for experience rating," Insurance: Mathematics and Economics, Elsevier, vol. 125(C).
    • Handle: RePEc:eee:insuma:v:125:y:2025:i:c:s0167668725000964
    DOI: 10.1016/j.insmatheco.2025.103149
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    References listed on IDEAS

    as
    1. Jung, Robert C. & Liesenfeld, Roman & Richard, Jean-François, 2011. "Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 73-85.
    2. Robert C. Jung & Roman Liesenfeld & Jean-François Richard, 2011. "Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 73-85, January.
    3. Qiao Jiang & Tianxiang Shi, 2024. "Auto Insurance Pricing Using Telematics Data: Application of a Hidden Markov Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 28(4), pages 822-839, October.
    4. Christian Gouriéroux & Yang Lu, 2019. "Negative Binomial Autoregressive Process with Stochastic Intensity," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(2), pages 225-247, March.
    5. Fokianos, Konstantinos, 2024. "Multivariate Count Time Series Modelling," Econometrics and Statistics, Elsevier, vol. 31(C), pages 100-116.
    6. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 407-417, October.
    7. René Ferland & Alain Latour & Driss Oraichi, 2006. "Integer‐Valued GARCH Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 923-942, November.
    8. Robin Henderson, 2003. "A serially correlated gamma frailty model for longitudinal count data," Biometrika, Biometrika Trust, vol. 90(2), pages 355-366, June.
    9. Edward Frees & Ping Wang, 2005. "Credibility Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(2), pages 31-48.
    10. Sundt, Bjorn, 1988. "Credibility estimators with geometric weights," Insurance: Mathematics and Economics, Elsevier, vol. 7(2), pages 113-122, April.
    11. Aknouche, Abdelhakim & Francq, Christian, 2021. "Count And Duration Time Series With Equal Conditional Stochastic And Mean Orders," Econometric Theory, Cambridge University Press, vol. 37(2), pages 248-280, April.
    12. Natacha Brouhns & Montserrat Guillén & Michel Denuit & Jean Pinquet, 2003. "Bonus‐Malus Scales in Segmented Tariffs With Stochastic Migration Between Segments," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 70(4), pages 577-599, December.
    13. Fukang Zhu, 2011. "A negative binomial integer‐valued GARCH model," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(1), pages 54-67, January.
    14. Pinquet, Jean & Guillén, Montserrat & Bolancé, Catalina, 2001. "Allowance for the Age of Claims in Bonus-Malus Systems," ASTIN Bulletin, Cambridge University Press, vol. 31(2), pages 337-348, November.
    15. Jae Youn Ahn & Himchan Jeong & Yang Lu, 2023. "A simple Bayesian state-space approach to the collective risk models," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2023(5), pages 509-529, May.
    16. 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.
    17. Yanez, Juan Sebastian & Guillén, Montserrat & Nielsen, Jens Perch, 2025. "Weekly dynamic motor insurance ratemaking with a telematics signals bonus-malus score," ASTIN Bulletin, Cambridge University Press, vol. 55(1), pages 1-28, January.
    18. Purcaru, Oana & Denuit, Michel, 2003. "Dependence in Dynamic Claim Frequency Credibility Models," ASTIN Bulletin, Cambridge University Press, vol. 33(1), pages 23-40, May.
    19. Chan, Ian Weng & Badescu, Andrei L. & Lin, X. Sheldon, 2025. "Assessing driving risk through unsupervised detection of anomalies in telematics time series data," ASTIN Bulletin, Cambridge University Press, vol. 55(2), pages 205-241, May.
    20. Dani Gamerman & Thiago Rezende Santos & Glaura C. Franco, 2013. "A Non-Gaussian Family Of State-Space Models With Exact Marginal Likelihood," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 625-645, November.
    21. Yunwei Cui & Robert Lund, 2009. "A new look at time series of counts," Biometrika, Biometrika Trust, vol. 96(4), pages 781-792.
    22. Genest, Christian & Nešlehová, Johanna, 2007. "A Primer on Copulas for Count Data," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 475-515, November.
    23. Yisu Jia & Stefanos Kechagias & James Livsey & Robert Lund & Vladas Pipiras, 2023. "Latent Gaussian Count Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(541), pages 596-606, January.
    24. Abdallah, Anas & Boucher, Jean-Philippe & Cossette, Hélène, 2016. "Sarmanov family of multivariate distributions for bivariate dynamic claim counts model," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 120-133.
    25. Lu Yang, 2022. "Nonparametric Copula Estimation for Mixed Insurance Claim Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(2), pages 537-546, April.
    26. Sylvia FrüHwirth-Schnatter & Helga Wagner, 2006. "Auxiliary mixture sampling for parameter-driven models of time series of counts with applications to state space modelling," Biometrika, Biometrika Trust, vol. 93(4), pages 827-841, December.
    27. Dionne, Georges & Vanasse, Charles, 1989. "A Generalization of Automobile Insurance Rating Models: The Negative Binomial Distribution with a Regression Component," ASTIN Bulletin, Cambridge University Press, vol. 19(2), pages 199-212, November.
    28. Vasiliki Christou & Konstantinos Fokianos, 2014. "Quasi-Likelihood Inference For Negative Binomial Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(1), pages 55-78, January.
    29. Debaly, Zinsou Max & Truquet, Lionel, 2021. "Iterations Of Dependent Random Maps And Exogeneity In Nonlinear Dynamics," Econometric Theory, Cambridge University Press, vol. 37(6), pages 1135-1172, December.
    30. Xu, Hai-Yan & Xie, Min & Goh, Thong Ngee & Fu, Xiuju, 2012. "A model for integer-valued time series with conditional overdispersion," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4229-4242.
    31. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 422-422, October.
    32. 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.
    33. Shi, Yue & Punzo, Antonio & Otneim, Håkon & Maruotti, Antonello, 2025. "Hidden semi-Markov models for rainfall-related insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 120(C), pages 91-106.
    34. Edward W. Frees & Gee Lee & Lu Yang, 2016. "Multivariate Frequency-Severity Regression Models in Insurance," Risks, MDPI, vol. 4(1), pages 1-36, February.
    35. E. Gonçalves & N. Mendes-Lopes & F. Silva, 2015. "Infinitely Divisible Distributions in Integer-Valued Garch Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(4), pages 503-527, July.
    36. Duval, Francis & Boucher, Jean-Philippe & Pigeon, Mathieu, 2024. "Telematics combined actuarial neural networks for cross-sectional and longitudinal claim count data," ASTIN Bulletin, Cambridge University Press, vol. 54(2), pages 239-262, May.
    37. Pinquet, Jean, 2020. "Positivity properties of the ARFIMA(0,d,0) specifications and credibility analysis of frequency risks," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 159-165.
    38. Richard A. Davis & Rongning Wu, 2009. "A negative binomial model for time series of counts," Biometrika, Biometrika Trust, vol. 96(3), pages 735-749.
    39. Tsz Chai Fung & Yinhuan Li & Liang Peng & Linyi Qian, 2024. "Testing Constant Serial Dynamics in Two-Step Risk Inference for Longitudinal Actuarial Data," North American Actuarial Journal, Taylor & Francis Journals, vol. 28(4), pages 861-881, October.
    40. Yang Lu, 2018. "Dynamic Frailty Count Process in Insurance: A Unified Framework for Estimation, Pricing, and Forecasting," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(4), pages 1083-1102, December.
    41. Pinquet, Jean, 2020. "Poisson Models With Dynamic Random Effects And Nonnegative Credibilities Per Period," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 585-618, May.
    42. Ali Ahmad & Christian Francq, 2016. "Poisson QMLE of Count Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 291-314, May.
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    Keywords

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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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