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To model high dimensional data, Gaussian methods are widely used since theyremain tractable and yield parsimonious models by imposing strong assumptionson the data. Vine copulas are more flexible by combining arbitrary marginaldistributions and (conditional) bivariate copulas. Yet, this adaptability isaccompanied by sharply increasing computational effort as the dimensionincreases. The approach proposed in this paper overcomes this burden and makesthe first step into ultra high dimensional non-Gaussian dependence modeling byusing a divide-and-conquer approach. First, we apply Gaussian methods to splitdatasets into feasibly small subsets and second, apply parsimonious andflexible vine copulas thereon. Finally, we reconcile them into one joint model.We provide numerical results demonstrating the feasibility of our approach inmoderate dimensions and showcase its ability to estimate ultra high dimensionalnon-Gaussian dependence models in thousands of dimensions.

Dependence Modeling in Ultra High Dimensions with Vine Copulas and the Graphical Lasso