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We propose a novel structure selection method for high dimensional (d > 100)sparse vine copulas. Current sequential greedy approaches for structureselection require calculating spanning trees in hundreds of dimensions andfitting the pair copulas and their parameters iteratively throughout thestructure selection process. Our method uses a connection between the vine andstructural equation models (SEMs). The later can be estimated very fast usingthe Lasso, also in very high dimensions, to obtain sparse models. Thus, weobtain a structure estimate independently of the chosen pair copulas andparameters. Additionally, we define the novel concept of regularization pathsfor R-vine matrices. It relates sparsity of the vine copula model in terms ofindependence copulas to a penalization coefficient in the structural equationmodels. We illustrate our approach and provide many numerical examples. Theseinclude simulations and data applications in high dimensions, showing thesuperiority of our approach to other existing methods.

Selection of Sparse Vine Copulas in High Dimensions with the Lasso