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t-copula from the viewpoint of tail dependence matrices

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  • Shyamalkumar, Nariankadu D.
  • Tao, Siyang

Abstract

The tail dependence coefficient is a bivariate measure of dependence in the tail, and the Tail Dependence Matrix (TDM) is a bidimensional array of these coefficients corresponding to a random vector. The TDM serves as a parsimonious measure of multivariate tail dependence akin to the correlation matrix in the context of dependence. The set of all TDMs corresponding to d-dimensional random vectors is a convex polytope with an intricate description known only for d up to six, with both its numbers of facets and vertices growing at least exponentially in d. We posit that the richness of its subset that a copula family can accommodate is a practically vital feature to be considered in its choice for modeling in the presence of tail dependence. In this paper, our focus is on the t-copula family, which is a popular choice for parametric modeling in risk management and financial econometrics. We discuss some geometric properties of the subset of TDMs supported by the t-copula family and provide an efficient algorithm to determine the t-copula that best captures the tail dependence specified by a target TDM.

Suggested Citation

  • Shyamalkumar, Nariankadu D. & Tao, Siyang, 2022. "t-copula from the viewpoint of tail dependence matrices," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    • Handle: RePEc:eee:jmvana:v:191:y:2022:i:c:s0047259x22000471
    DOI: 10.1016/j.jmva.2022.105027
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    References listed on IDEAS

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