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Title: Non-central squared copulas: properties and applications

The goal of this presentation is to introduce new families of multivariate copulas, extending the chi-square copulas, the Fisher copula, and squared copulas. The new families are constructed from existing copulas by first transforming their margins to standard Gaussian distributions, then transforming these variables into non-central chi-square variables with one degree of freedom, and finally by considering the copula associated with these new variables. It is shown that by varying the non-centrality parameters, one can model non-monotonic dependence, and when one or many non-centrality parameters are outside a given hyper-rectangle, then the copula is almost the same as the one when these parameters are infinite. For these new families, the tail behavior, the monotonicity of dependence measures such as Kendall鈥檚 tau and Spearman鈥檚 rho are investigated, and estimation is discussed. Some examples will illustrate the usefulness of these new copula families.

Bouchra Nasri is a postdoctoral fellow in the Department of Mathematics and Statistics at McGill, under the supervision of Professor Christian Genest. Her research interests include conditional distributions, dependence models, big data, and time series.