Practical Notes On Multivariate Modeling Based on Elliptical Copulas

Xiaojing Wang, Jun Yan


Multivariate distributions based on elliptical copulas have been widely used in many fields such as hydrology
and finance. We focus on two practical issues of applications of such models. The first is a caveat rooted in a
consistency property defined by Kano (1994, Journal of Multivariate Analysis, 51:139–147) for elliptical distributions.
Some elliptical families do not have this property, which puts practical limitations on applications and software
implementation of the corresponding elliptical copulas. The second issue is on conditional sampling from such
distributions, which is important in Monte Carlo statistical inferences, especially when closed-form solutions are
not available or feasible. Two sampling methods are presented: a direct sampling approach based on a stochastic
representation of elliptical distributions, and an acceptance/rejection sampling method. The latter also provides an
importance sampler as a byproduct, which may have higher efficiency for some applications. A trivariate model of the
volume, duration, and peak intensity of annual extreme storms illustrates the sampling algorithms.

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SFdS / SMF - Journal de la Société Française de Statistique - ISSN 2102-6238