IDEAS home Printed from
   My bibliography  Save this article

Penalized marginal likelihood estimation of finite mixtures of Archimedean copulas


  • Göran Kauermann


  • Renate Meyer


This paper proposes finite mixtures of different Archimedean copula families as a flexible tool for modelling the dependence structure in multivariate data. A novel approach to estimating the parameters in this mixture model is presented by maximizing the penalized marginal likelihood via iterative quadratic programming. The motivation for the penalized marginal likelihood stems from an underlying Bayesian model that imposes a prior distribution on the parameter of each Archimedean copula family. An approximative marginal likelihood is obtained by a classical quadrature discretization of the integral w.r.t. each family-specific prior distribution, thus yielding a finite mixture model. Family-specific smoothness penalties are added and the penalized marginal likelihood is maximized using an iterative quadratic programming routine. For comparison purposes, we also present a fully Bayesian approach via simulation-based posterior computation. The performance of the novel estimation approach is evaluated by simulations and two examples involving the modelling of the interdependence of exchange rates and of wind speed measurements, respectively. For these examples, penalized marginal likelihood estimates are compared to the corresponding Bayesian estimates. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Göran Kauermann & Renate Meyer, 2014. "Penalized marginal likelihood estimation of finite mixtures of Archimedean copulas," Computational Statistics, Springer, vol. 29(1), pages 283-306, February.
  • Handle: RePEc:spr:compst:v:29:y:2014:i:1:p:283-306
    DOI: 10.1007/s00180-013-0454-1

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

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

    References listed on IDEAS

    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    2. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    3. Yan, Jun, 2007. "Enjoy the Joy of Copulas: With a Package copula," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 21(i04).
    4. Hofert, Marius & Maechler, Martin, 2011. "Nested Archimedean Copulas Meet R: The nacopula Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i09).
    5. Cornelia Savu & Mark Trede, 2010. "Hierarchies of Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 295-304.
    6. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    7. Lambert, Philippe, 2007. "Archimedean copula estimation using Bayesian splines smoothing techniques," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6307-6320, August.
    8. Kjersti Aas & Daniel Berg, 2009. "Models for construction of multivariate dependence - a comparison study," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 639-659.
    9. Komárek, Arnost & Lesaffre, Emmanuel, 2008. "Generalized linear mixed model with a penalized Gaussian mixture as a random effects distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3441-3458, March.
    10. Nikolay Nenovsky & S. Statev, 2006. "Introduction," Post-Print halshs-00260898, HAL.
    11. Ostap Okhrin & Yarema Okhrin & Wolfgang Schmid, 2009. "Properties of Hierarchical Archimedean Copulas," SFB 649 Discussion Papers SFB649DP2009-014, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    12. Peter X.-K. Song & Mingyao Li & Ying Yuan, 2009. "Joint Regression Analysis of Correlated Data Using Gaussian Copulas," Biometrics, The International Biometric Society, vol. 65(1), pages 60-68, March.
    13. Wolfgang Härdle & Ostap Okhrin, 2010. "De copulis non est disputandum," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(1), pages 1-31, March.
    14. Ling Hu, 2006. "Dependence patterns across financial markets: a mixed copula approach," Applied Financial Economics, Taylor & Francis Journals, vol. 16(10), pages 717-729.
    15. Göran Kauermann & Tatyana Krivobokova & Ludwig Fahrmeir, 2009. "Some asymptotic results on generalized penalized spline smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 487-503.
    16. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    17. Paul Embrechts, 2009. "Copulas: A Personal View," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 639-650.
    Full references (including those not matched with items on IDEAS)


    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:29:y:2014:i:1:p:283-306. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.