  Vine copulas allow to build flexible dependence models for an arbitrary
number of variables using only bivariate building blocks. The number of
parameters in a vine copula model increases quadratically with the dimension,
which poses new challenges in high-dimensional applications. To alleviate the
computational burden and risk of overfitting, we propose a modified Bayesian
information criterion (BIC) tailored to sparse vine copula models. We show that
the criterion can consistently distinguish between the true and alternative
models under less stringent conditions than the classical BIC. The new
criterion can be used to select the hyper-parameters of sparse model classes,
such as truncated and thresholded vine copulas. We propose a computationally
efficient implementation and illustrate the benefits of the new concepts with a
case study where we model the dependence in a large stock stock portfolio.
