Multivariate Distributions Through Pair-Copula Construction: Theory and Applications

Abstract

It is often very difficult, particularly in higher dimensions, to find a good multivariate model that describes both marginal behavior and dependence structure of data efficiently. The copula approach to multivariate models has been found to fit this purpose particularly well, and since it is a relatively new concept in statistical modeling, it is under frequent development. In this thesis we focus on the decomposition of a multivariate model into pairwise copulas rather than the usual multivariate copula approach. We account for the theory behind the decomposition of a multivariate model into pairwise copulas, and apply the theory on both daily and intra day financial returns. The results are compared with the usual multivariate copula approach, and problems applying the theory are accounted for. The multivariate copula is rejected in favor of the pairwise decomposed model on daily returns with a level of significance less than 1%, while our decomposed models on intra day data does not lead to a rejection of the models with multivariate copulas. On daily returns a pairwise decomposition with Student copulas is preferable to multivariate copulas, while the decomposed models on intra day data need more development before outperforming multivariate copulas.