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Abstract:
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Archimedean copulas constitute an important class of dependence structures, mainly because of their simple algebraic form which makes dependence characteristics more tractable and opens possibilities for feasible statistical inference. In this talk, we focus on Archimedean copulas in high dimensions whose generators are arbitrary and provide necessary and sufficient conditions for their existence. We will also show that Archimedean copulas are naturally linked to simplex distributions. This allows for generalizations of numerous results from the bivariate case to any dimension, for easy construction of new families and for a feasible simulation procedure. Finally, implications for extreme-value dependence will be explored, along with generalizations to asymmetric copula families.
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