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EM estimation for bivariate mixed poisson INAR(1) claim count regression models with correlated random effects

Author

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  • Chen, Zezhun Chen
  • Dassios, Angelos
  • Tzougas, George

Abstract

This article considers bivariate mixed Poisson INAR(1) regression models with correlated random effects for modelling correlations of different signs and magnitude among time series of different types of claim counts. This is the first time that the proposed family of INAR(1) models is used in a statistical or actuarial context. For expository purposes, the bivariate mixed Poisson INAR(1) claim count regression models with correlated Lognormal and Gamma random effects paired via a Gaussian copula are presented as competitive alternatives to the classical bivariate Negative Binomial INAR(1) claim count regression model which only allows for positive dependence between the time series of claim count responses. Our main achievement is that we develop novel alternative Expectation-Maximization type algorithms for maximum likelihood estimation of the parameters of the models which are demonstrated to perform satisfactory when the models are fitted to Local Government Property Insurance Fund data from the state of Wisconsin.

Suggested Citation

  • Chen, Zezhun Chen & Dassios, Angelos & Tzougas, George, 2023. "EM estimation for bivariate mixed poisson INAR(1) claim count regression models with correlated random effects," LSE Research Online Documents on Economics 118826, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:118826
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    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. Pechon, Florian & Denuit, Michel & Trufin, Julien, 2021. "Home and Motor insurance joined at a household level using multivariate credibility," Annals of Actuarial Science, Cambridge University Press, vol. 15(1), pages 82-114, March.
    5. Denuit, Michel & Guillen, Montserrat & Trufin, Julien, 2019. "Multivariate credibility modelling for usage-based motor insurance pricing with behavioural data," LIDAM Reprints ISBA 2019039, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Aristidis Nikoloulopoulos & Dimitris Karlis, 2010. "Regression in a copula model for bivariate count data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1555-1568.
    7. Genest, Christian & Nešlehová, Johanna, 2007. "A Primer on Copulas for Count Data," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 475-515, November.
    8. Bolancé, Catalina & Vernic, Raluca, 2019. "Multivariate count data generalized linear models: Three approaches based on the Sarmanov distribution," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 89-103.
    9. Denuit, Michel & Guillen, Montserrat & Trufin, Julien, 2019. "Multivariate credibility modelling for usage-based motor insurance pricing with behavioural data," Annals of Actuarial Science, Cambridge University Press, vol. 13(2), pages 378-399, September.
    10. Gurmu, Shiferaw & Elder, John, 2000. "Generalized bivariate count data regression models," Economics Letters, Elsevier, vol. 68(1), pages 31-36, July.
    11. Anas Abdallah & Jean-Philippe Boucher & Hélène Cossette & Julien Trufin, 2016. "Sarmanov Family of Bivariate Distributions for Multivariate Loss Reserving Analysis," North American Actuarial Journal, Taylor & Francis Journals, vol. 20(2), pages 184-200, April.
    12. Lluís Bermúdez & Dimitris Karlis, 2021. "Multivariate INAR(1) Regression Models Based on the Sarmanov Distribution," Mathematics, MDPI, vol. 9(5), pages 1-13, March.
    13. Chai Fung, Tsz & Badescu, Andrei L. & Sheldon Lin, X., 2019. "A Class Of Mixture Of Experts Models For General Insurance: Application To Correlated Claim Frequencies," ASTIN Bulletin, Cambridge University Press, vol. 49(3), pages 647-688, September.
    14. Xanthi Pedeli & Dimitris Karlis, 2013. "On composite likelihood estimation of a multivariate INAR(1) model," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(2), pages 206-220, March.
    15. Shi, Peng & Valdez, Emiliano A., 2014. "Multivariate negative binomial models for insurance claim counts," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 18-29.
    16. A. Colin Cameron & Tong Li & Pravin K. Trivedi & David M. Zimmer, 2004. "Modelling the differences in counted outcomes using bivariate copula models with application to mismeasured counts," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 566-584, December.
    17. Pechon, Florian & Denuit, Michel & Trufin, Julien, 2019. "Multivariate modelling of multiple guarantees in motor insurance of a household," LIDAM Reprints ISBA 2019031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    18. Bermúdez, Lluís & Guillén, Montserrat & Karlis, Dimitris, 2018. "Allowing for time and cross dependence assumptions between claim counts in ratemaking models," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 161-169.
    19. Pechon, Florian & Denuit, Michel & Trufin, Julien, 2021. "Home and Motor insurance joined at a household level using multivariate credibility," LIDAM Reprints ISBA 2021007, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    20. 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.
    21. Edward W. Frees & Gee Lee & Lu Yang, 2016. "Multivariate Frequency-Severity Regression Models in Insurance," Risks, MDPI, vol. 4(1), pages 1-36, February.
    22. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
    23. Fung, Tsz Chai & Badescu, Andrei L. & Lin, X. Sheldon, 2019. "A class of mixture of experts models for general insurance: Theoretical developments," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 111-127.
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    More about this item

    Keywords

    count data time series; Binomial-mixed Poisson INAR(1) regression models with correlated random effects; overdispersion; Gaussian copula; correlations of different signs and magnitude; Springer deal;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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