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