Siyang Tao EVA Talk Preview
From Anna Munro
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Name: Siyang Tao
Talk Title: On Modeling Tail Dependence via t-copula
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 that is known only for d less than or equal to six. In particular, both the numbers of facets and vertices of the set of all TDMs grow exponentially in d. We posit that the richness of the subset of the set of all TDMs that can be accommodated by a copula family is a practically important feature in its choice for modeling in the presence of tail dependence. In this talk, our focus is on the t-copula family that is a popular choice, especially in the presence of tail dependence, in many areas of statistical modeling including risk management and financial econometrics. We discuss some geometric properties of the subset of the set of all TDMs that is supported by the t-copula family and provide an efficient algorithm to determine the t-copula that best captures the tail dependence specified using a target TDM.
This talk is a contributed talk at EVA 2021. View the programme here.