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Multivariate INAR(1) Regression Models Based on the Sarmanov Distribution

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  • Lluís Bermúdez

    (Departament de Matemàtica Econòmica, Financera i Actuarial, Riskcenter-IREA, University of Barcelona, Av. Diagonal, 690, 08034 Barcelona, Spain
    These authors contributed equally to this work.)

  • Dimitris Karlis

    (Department of Statistics, Athens University of Economics and Business, 2, Troias, Kimolou & Spetson Str., 113 62 Athens, Greece
    These authors contributed equally to this work.)

Abstract

A multivariate INAR(1) regression model based on the Sarmanov distribution is proposed for modelling claim counts from an automobile insurance contract with different types of coverage. The correlation between claims from different coverage types is considered jointly with the serial correlation between the observations of the same policyholder observed over time. Several models based on the multivariate Sarmanov distribution are analyzed. The new models offer some advantages since they have all the advantages of the MINAR(1) regression model but allow for a more flexible dependence structure by using the Sarmanov distribution. Driven by a real panel data set, these models are considered and fitted to the data to discuss their goodness of fit and computational efficiency.

Suggested Citation

  • Lluís Bermúdez & Dimitris Karlis, 2021. "Multivariate INAR(1) Regression Models Based on the Sarmanov Distribution," Mathematics, MDPI, vol. 9(5), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:505-:d:508246
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    References listed on IDEAS

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    1. Vernic, Raluca, 2018. "On the evaluation of some multivariate compound distributions with Sarmanov’s counting distribution," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 184-193.
    2. Liu, Feng & Pitt, David, 2017. "Application of bivariate negative binomial regression model in analysing insurance count data," Annals of Actuarial Science, Cambridge University Press, vol. 11(2), pages 390-411, September.
    3. Vera Hofer & Johannes Leitner, 2012. "A bivariate Sarmanov regression model for count data with generalised Poisson marginals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(12), pages 2599-2617, August.
    4. Felix Famoye, 2010. "A new bivariate generalized Poisson distribution," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(1), pages 112-124, February.
    5. José Rodríguez-Lallena & Manuel Úbeda-Flores, 2010. "Multivariate copulas with quadratic sections in one variable," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(3), pages 331-349, November.
    6. 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.
    7. Pedeli, Xanthi & Karlis, Dimitris, 2013. "Some properties of multivariate INAR(1) processes," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 213-225.
    8. Felix Famoye, 2015. "A Multivariate Generalized Poisson Regression Model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(3), pages 497-511, February.
    9. Felix Famoye, 2019. "Bivariate exponentiated‐exponential geometric regression model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 73(3), pages 434-450, August.
    10. Bermúdez, Lluís & Karlis, Dimitris, 2012. "A finite mixture of bivariate Poisson regression models with an application to insurance ratemaking," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3988-3999.
    11. Gómez-Déniz, Emilio & Sarabia, José María & Balakrishnan, N., 2012. "A Multivariate Discrete Poisson-Lindley Distribution: Extensions and Actuarial Applications," ASTIN Bulletin, Cambridge University Press, vol. 42(2), pages 655-678, November.
    12. Miravete, Eugenio, 2009. "Multivariate Sarmanov Count Data Models," CEPR Discussion Papers 7463, C.E.P.R. Discussion Papers.
    13. 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.
    14. Yan Cui & Fukang Zhu, 2018. "A new bivariate integer-valued GARCH model allowing for negative cross-correlation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 428-452, June.
    15. Felix Famoye, 2010. "On the bivariate negative binomial regression model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(6), pages 969-981.
    16. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
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    Cited by:

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    2. 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.

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