IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v38y2023i2d10.1007_s00180-022-01253-0.html
   My bibliography  Save this article

Multivariate mixed Poisson Generalized Inverse Gaussian INAR(1) regression

Author

Listed:
  • Zezhun Chen

    (London School of Economics)

  • Angelos Dassios

    (London School of Economics)

  • George Tzougas

    (Heriot-Watt University)

Abstract

In this paper, we present a novel family of multivariate mixed Poisson-Generalized Inverse Gaussian INAR(1), MMPGIG-INAR(1), regression models for modelling time series of overdispersed count response variables in a versatile manner. The statistical properties associated with the proposed family of models are discussed and we derive the joint distribution of innovations across all the sequences. Finally, for illustrative purposes different members of the MMPGIG-INAR(1) class are fitted to Local Government Property Insurance Fund data from the state of Wisconsin via maximum likelihood estimation.

Suggested Citation

  • Zezhun Chen & Angelos Dassios & George Tzougas, 2023. "Multivariate mixed Poisson Generalized Inverse Gaussian INAR(1) regression," Computational Statistics, Springer, vol. 38(2), pages 955-977, June.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:2:d:10.1007_s00180-022-01253-0
    DOI: 10.1007/s00180-022-01253-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-022-01253-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-022-01253-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Annika Homburg & Christian H. Weiß & Layth C. Alwan & Gabriel Frahm & Rainer Göb, 2019. "Evaluating Approximate Point Forecasting of Count Processes," Econometrics, MDPI, vol. 7(3), pages 1-28, July.
    2. 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).
    3. Predrag M. Popović & Miroslav M. Ristić & Aleksandar S. Nastić, 2016. "A geometric bivariate time series with different marginal parameters," Statistical Papers, Springer, vol. 57(3), pages 731-753, September.
    4. 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.
    5. 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.
    6. 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).
    7. Christian Weiß, 2008. "Thinning operations for modeling time series of counts—a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(3), pages 319-341, August.
    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. Aleksandar S. Nastić & Miroslav M. Ristić & Predrag M. Popović, 2016. "Estimation in a bivariate integer-valued autoregressive process," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(19), pages 5660-5678, October.
    10. 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.
    11. Lluís Bermúdez & Dimitris Karlis, 2021. "Multivariate INAR(1) Regression Models Based on the Sarmanov Distribution," Mathematics, MDPI, vol. 9(5), pages 1-13, March.
    12. 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.
    13. Lluís Bermúdez & Dimitris Karlis, 2017. "A posteriori ratemaking using bivariate Poisson models," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2017(2), pages 148-158, February.
    14. R. K. Freeland & B. P. M. McCabe, 2004. "Analysis of low count time series data by poisson autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 701-722, September.
    15. 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).
    16. 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.
    17. 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.
    18. 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).
    19. 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.
    20. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. George Tzougas & Despoina Makariou, 2022. "The multivariate Poisson‐Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 25(4), pages 401-417, December.
    2. Chen, Zezhun Chen & Dassios, Angelos & Tzougas, George, 2024. "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.
    3. Tzougas, George & Makariou, Despoina, 2022. "The multivariate Poisson-Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters," LSE Research Online Documents on Economics 117197, London School of Economics and Political Science, LSE Library.
    4. Michel Denuit & Yang Lu, 2021. "Wishart‐gamma random effects models with applications to nonlife insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(2), pages 443-481, June.
    5. Pechon, Florian & Denuit, Michel & Trufin, Julien, 2019. "Home and Motor insurance joined at a household level using multivariate credibility," LIDAM Discussion Papers ISBA 2019013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. 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.
    7. Tzougas, George & di Cerchiara, Alice Pignatelli, 2021. "Bivariate mixed Poisson regression models with varying dispersion," LSE Research Online Documents on Economics 114327, London School of Economics and Political Science, LSE Library.
    8. Lluís Bermúdez & Dimitris Karlis, 2021. "Multivariate INAR(1) Regression Models Based on the Sarmanov Distribution," Mathematics, MDPI, vol. 9(5), pages 1-13, March.
    9. Zezhun Chen & Angelos Dassios & George Tzougas, 2022. "EM Estimation for the Bivariate Mixed Exponential Regression Model," Risks, MDPI, vol. 10(5), pages 1-13, May.
    10. Pechon, Florian & Denuit, Michel & Trufin, Julien, 2018. "Multivariate Modelling of Multiple Guarantees in Motor Insurance of a Household," LIDAM Discussion Papers ISBA 2018019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Denuit, Michel & Lu, Yang, 2020. "Wishart-Gamma mixtures for multiperil experience ratemaking, frequency-severity experience rating and micro-loss reserving," LIDAM Discussion Papers ISBA 2020016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Ramon Alemany & Catalina Bolancé & Roberto Rodrigo & Raluca Vernic, 2020. "Bivariate Mixed Poisson and Normal Generalised Linear Models with Sarmanov Dependence—An Application to Model Claim Frequency and Optimal Transformed Average Severity," Mathematics, MDPI, vol. 9(1), pages 1-18, December.
    13. Chen, Zezhun & Dassios, Angelos & Tzougas, George, 2022. "EM estimation for the bivariate mixed exponential regression model," LSE Research Online Documents on Economics 115132, London School of Economics and Political Science, LSE Library.
    14. Dhiti Osatakul & Xueyuan Wu, 2021. "Discrete-Time Risk Models with Claim Correlated Premiums in a Markovian Environment," Risks, MDPI, vol. 9(1), pages 1-23, January.
    15. Kachour Maher & Bakouch Hassan S. & Mohammadi Zohreh, 2023. "A New INAR(1) Model for ℤ-Valued Time Series Using the Relative Binomial Thinning Operator," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 243(2), pages 125-152, April.
    16. Christian Weiß, 2015. "A Poisson INAR(1) model with serially dependent innovations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(7), pages 829-851, October.
    17. Catalina Bolancé & Raluca Vernic, 2017. "“Multivariate count data generalized linear models: Three approaches based on the Sarmanov distribution”," IREA Working Papers 201718, University of Barcelona, Research Institute of Applied Economics, revised Oct 2017.
    18. Nemanja Milanović & Miloš Milosavljević & Slađana Benković & Dušan Starčević & Željko Spasenić, 2020. "An Acceptance Approach for Novel Technologies in Car Insurance," Sustainability, MDPI, vol. 12(24), pages 1-15, December.
    19. José M. R. Murteira & Mário A. G. Augusto, 2017. "Hurdle models of repayment behaviour in personal loan contracts," Empirical Economics, Springer, vol. 53(2), pages 641-667, September.
    20. Montserrat Guillen & Jens Perch Nielsen & Ana M. Pérez‐Marín, 2021. "Near‐miss telematics in motor insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(3), pages 569-589, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:38:y:2023:i:2:d:10.1007_s00180-022-01253-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.