Um teste para dependência de valores extremos utilizando cópulas

Abstract

In the statistical modeling of risks, in the fields of finance and actuary, it is usual that the assumption of independent risks is adopted, or yet, to model the risks by a multivariate normal distribution. In practice, however, independence is exception and the multivariate normal distribution only captures linear dependence between risks, which, in reality, often exhibits complex dependence structures. Copulas are models that circumvents theses limitations, since they cover, besides linear dependence, nonlinear cases. Among several copula families, stands out extreme value copulas, which models variables/risks that show extreme value dependence, a particularly dangerous case for the risk analyst, once it represents large losses that could happen jointly. Therefore, it is important that extreme value dependence be detected in the process of risk assessment. Given that, using extreme value copulas, a new method was elaborated to test whether a bivariate dataset exhibits extreme value dependence. The test performed efficiently in most cases, keeping type I error rates close to the nominal level and being as powerful as the best tests.