Properties of hierarchical Archimedean copulas

Arbeitspapier

In this paper we analyse the properties of hierarchical Archimedean copulas. This class is a generalisation of the Archimedean opulas and allows for general non-exchangeable dependency structures. We show that the structure of the copula can be uniquely recovered from all bivariate margins. We derive the distribution of the copula value, which is particularly useful for tests and constructing confidence intervals. Furthermore, we analyse dependence orderings, multivariate dependence measures and extreme value copulas. Special attention we pay to the tail dependencies and derive several tail dependence indices for general hierarchical Archimedean copulas.

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• Language: Englisch

References and Relationships

• Bibliographic citation: Series: SFB 649 Discussion Paper ; No. 2009,014

Classification and Topics

• Classification: Wirtschaft ; Specific Distributions; Specific Statistics
• Subject: Copula ; multivariate distribution ; Archimedean copula ; stochastic ordering ; hierarchical copula ; Kopula (Mathematik) ; Multivariate Analyse ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Okhrin, Ostap ; Okhrin, Yarema ; Schmid, Wolfgang
• Event: Veröffentlichung
• (who): Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk
• (where): Berlin
• (when): 2009

Further information

• Handle: http://hdl.handle.net/10419/25330