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Penalized marginal likelihood estimation of finite mixtures of Archimedean copulas

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Abstract

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.

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Acknowledgments

The second author gratefully acknowledges the support of this research by a grant from the German Academic Exchange Service (DAAD) and an FRDF Grant of the University of Auckland.

The authors wish to acknowledge the contribution of the NeSI high-performance computing facilities and the staff at the Centre for eResearch at the University of Auckland.

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Authors and Affiliations

  1. Institut für Statistik, Ludwig-Maximilians-Universität München, Ludwigstrasse 33, 80539 , Munich, Germany

    Göran Kauermann

  2. Department of Statistics, University of Auckland, Private Bag 92019, Auckland, New Zealand

    Renate Meyer

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  1. Göran Kauermann
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  2. Renate Meyer
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Correspondence to Göran Kauermann.

Appendix

Appendix

1.1 WinBUGS code: mixture of bivariate copulas

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Kauermann, G., Meyer, R. Penalized marginal likelihood estimation of finite mixtures of Archimedean copulas. Comput Stat 29, 283–306 (2014). https://doi.org/10.1007/s00180-013-0454-1

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  • DOI: https://doi.org/10.1007/s00180-013-0454-1

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