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Dependence Comparisons of Vine Copulae with Four or More Variables

In: Dependence Modeling Vine Copula Handbook

Author

Listed:
  • Harry Joe

    (Department of Statistics, University of British Columbia, Vancover BC, Canada, V6T 1Z2, Canada)

Abstract

It is known that there is one equivalence class of regular vines for n = 3 and two equivalence classes for n = 4. Through an enumeration, we show that there are six equivalence classes for n = 5 with boundary classes of C-vines and D-vines, so that the dimension of n = 5 is manageable in terms of studying the intermediate regular vines. For vine copulae, which obtain from associating a bivariate copula with each pair in the vine, we develop an approach that leads to algorithms for C-vines, D-vines and intermediate vines. Some similarities between different vine copulae can be seen from how they are simulated. For Gaussian and non-Gaussian vines, we compare the marginal bivariate dependence of different vine copulae when the level ℓ bivariate linking copulae are all set at Cℓ, ℓ = 1,…, n − 1.

Suggested Citation

  • Harry Joe, 2010. "Dependence Comparisons of Vine Copulae with Four or More Variables," World Scientific Book Chapters, in: Dorota Kurowicka & Harry Joe (ed.), Dependence Modeling Vine Copula Handbook, chapter 7, pages 139-164, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814299886_0007
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