  Vine copulas are a flexible class of dependence models consisting of
bivariate building blocks and have proven to be particularly useful in high
dimensions. Classical model distance measures require multivariate integration
and thus suffer from the curse of dimensionality. In this paper we provide
numerically tractable methods to measure the distance between two vine copulas
even in high dimensions. For this purpose, we consecutively develop three new
distance measures based on the Kullback-Leibler distance, using the result that
it can be expressed as the sum over expectations of KL distances between
univariate conditional densities, which can be easily obtained for vine
copulas. To reduce numerical calculations we approximate these expectations on
adequately designed grids, outperforming Monte Carlo-integration with respect
to computational time. In numerous examples and applications we illustrate the
strengths and weaknesses of the developed distance measures.
