Say a process exhibits ARCH/GARCH type non-linear dependence and we wish to evaluate its joint CDF. Without relying on a criterion, such as AIC what is the best copula family that fits this framework? I was thinking perhaps normal marginals and the Gumbel copula?
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Selecting the best-fit copula family is an important step in the copula model. One way to select the best-fit copula is by using a scatter plot to identify the shape of the dependency structures. In addition, the misspecification of the margins may lead to inaccurate results.
