Discussion of ‘Copulas: Tales and facts,’ by T. Mikosch
The essence of the provocative statements in Mikosch (2005) is that copulas do not add much to our understanding of multivariate probabilistic questions. When first presented at the 4th International Conference on Extreme Value Analysis in Gothenburg, 15–19 August 2005, most discussants agreed with this conclusion. We do not necessarily disagree, but in the interest of the intellectual debate, we nevertheless want to advance a few arguments in defense of the copula concept. Copulas are a way to separate the dependence structure from the marginal probabilities. In our discussion, we first give two examples from economics as to how this separation can be useful. Subsequently, we argue that if one tries to model the dependence structure, the use of a specific copula should be motivated by the problem at hand.