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Multivariate Markov Families of Copulas

Author

Listed:
  • Overbeck Ludger

    (Justus-Liebig Universität Gießen, Institut of Mathematics, 35392 Gießen)

  • Schmidt Wolfgang M.

    (Frankfurt School of Finance and Management, Sonnemannstr. 9-11, 60314 Frankfurt am Main)

Abstract

For the Markov property of a multivariate process, a necessary and suficient condition on the multidimensional copula of the finite-dimensional distributions is given. This establishes that the Markov property is solely a property of the copula, i.e., of the dependence structure. This extends results by Darsow et al. [11] from dimension one to the multivariate case. In addition to the one-dimensional case also the spatial copula between the different dimensions has to be taken into account. Examples are also given.

Suggested Citation

  • Overbeck Ludger & Schmidt Wolfgang M., 2015. "Multivariate Markov Families of Copulas," Dependence Modeling, De Gruyter, vol. 3(1), pages 1-13, October.
    • Handle: RePEc:vrs:demode:v:3:y:2015:i:1:p:13:n:11
    DOI: 10.1515/demo-2015-0011
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    References listed on IDEAS

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    4. Rémillard, Bruno & Papageorgiou, Nicolas & Soustra, Frédéric, 2012. "Copula-based semiparametric models for multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 30-42.
    5. Brendan K. Beare & Juwon Seo, 2015. "Vine Copula Specifications for Stationary Multivariate Markov Chains," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 228-246, March.
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