New Families of Copulas Based on Periodic Functions
by Aurélien Alfonsi of Ecole Nationale des Ponts et Chaussées, and
December 19, 2005
Abstract: Although there exists a large variety of copula functions, only a few are practically manageable, and often the choice in dependence modeling falls on the Gaussian copula. Further, most copulas are exchangeable, thus implying symmetric dependence. We introduce a way to construct copulas based on periodic functions. We study the two dimensional case based on one dependence parameter and then provide a way to extend the construction to the n dimensional framework. We can thus construct families of copulas in dimension n and parameterized by n - 1 parameters, implying possibly asymmetric relations. Such "periodic" copulas can be simulated easily.
Keywords: copula functions, non-exchangeable copulas.
Published in: Communications in Statistics: Theory and Methods, Vol. 34, No. 7, (2005), pp. 1437-1447.