Mixture copulas and the housing crisis

The use of copulas in order to model time series is gaining popularity due to its simplicity. Namely, marginal distributions can be obtained from the joint distribution based on some dependence structure and vice versa. An example of an application is Zimmer (2012), who used the copula approach to model dependencies of housing prices in the states Arizona, California, Florida and Nevada, which is important for risk estimation purposes. Previously this was modeled by a Gaussian copula, but this does not allow to model extreme events, like a crisis. Therefore, Zimmer tested several other copulas on filtered quarterly percentage changes of the Housing Price Index and found that a Clayton-Gumbel copula, which is a convex combination of copulas, i.e. a mixture copula, performed better than the Gaussian one. Since Zimmer (2012) tested only one mixture copula, he suggested that a Clayton-survival Clayton or Gumbel-survival Gumbel mixture might outperform the Clayton-Gumbel one. In this thesis, Zimmer’s suggestions are tested by adhering to his approach. It follows from Bayes Information Criterion and the Vuong test statistics that the suggested mixture copulas perform similarly to the Clayton-Gumbel one and that the captured tail-dependencies (or extreme observations) do not differ significantly across the copula mixtures.