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Vine Constructions of Levy Copulas

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  • Oliver Grothe
  • Stephan Nicklas
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    Abstract

    Levy copulas are the most general concept to capture jump dependence in multivariate Levy processes. They translate the intuition and many features of the copula concept into a time series setting. A challenge faced by both, distributional and Levy copulas, is to find flexible but still applicable models for higher dimensions. To overcome this problem, the concept of pair copula constructions has been successfully applied to distributional copulas. In this paper, we develop the pair construction for Levy copulas (PLCC). Similar to pair constructions of distributional copulas, the pair construction of a d-dimensional Levy copula consists of d(d-1)/2 bivariate dependence functions. We show that only d-1 of these bivariate functions are Levy copulas, whereas the remaining functions are distributional copulas. Since there are no restrictions concerning the choice of the copulas, the proposed pair construction adds the desired flexibility to Levy copula models. We discuss estimation and simulation in detail and apply the pair construction in a simulation study.

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    File URL: http://arxiv.org/pdf/1207.4309
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1207.4309.

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    Date of creation: Jul 2012
    Date of revision: Sep 2012
    Handle: RePEc:arx:papers:1207.4309

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    Web page: http://arxiv.org/

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    1. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    2. Kallsen, Jan & Tankov, Peter, 2006. "Characterization of dependence of multidimensional Lévy processes using Lévy copulas," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 97(7), pages 1551-1572, August.
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