The multivariate Piecing-Together approach revisited

Stefan Aulbach, Michael Falk and Martin Hofmann

Journal of Multivariate Analysis, 2012, vol. 110, issue C, 161-170

Abstract: The univariate Piecing-Together approach (PT) fits a univariate generalized Pareto distribution (GPD) to the upper tail of a given distribution function in a continuous manner. A multivariate extension was established by Aulbach et al. (in press) [2]: the upper tail of a given copula C is cut off and replaced by a multivariate GPD-copula in a continuous manner, yielding a new copula called a PT-copula. Then each margin of this PT-copula is transformed by a given univariate distribution function. This provides a multivariate distribution function with prescribed margins, whose copula is a GPD-copula that coincides in its central part with C. In addition to Aulbach et al. (in press) [2], we achieve in the present paper an exact representation of the PT-copula’s upper tail, giving further insight into the multivariate PT approach. A variant based on the empirical copula is also added. Furthermore our findings enable us to establish a functional PT version as well.

Keywords: Copula; Copula process; D-norm; Domain of multivariate attraction; Empirical copula; GPD-copula; Max-stable process; Multivariate extreme value distribution; Multivariate generalized Pareto distribution; Peaks-over-threshold; Piecing-Together approach (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.jmva.2012.02.002

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