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Abstract:
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Copulas are useful in the study of extreme values. Common statistical models for extremes are concerned with a univariate response, and copulas provide a simple way to incorporate dependence between variables whose marginal distributions are fit with classical extremes methodologies. Researchers have proposed measures of tail dependence to discern the joint behavior of variables in the tails of their distributions. In the case of bivariate copulas, tail dependence is usually focused on the "major-diagonal"--that is, when either both variables are simultaneously far in their upper tail or far in their lower tail. Motivated by the polar vortex phenomenon in North America, where very low temperatures in the Midwest coincide with very high temperatures in Alaska, we focus on "minor-diagonal" tail dependence, i.e., when one variable is far in its lower tail while the other is far in its upper tail. In particular, we seek a bivariate copula which has flexible tail behavior in all four corners of the unit square. To this end, we present a new modification of the student-t copula and show how a mixture of rotations of the proposed copula can capture various tail dependencies.
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