Truncating Regular Vine Copula Based on Mutual Information: An Efficient Parsimonious Model for High-Dimensional Data

Abstract

Based on (different) bivariate copulas as simple building blocks to model complex multivariate dependency patterns, vine copulas provide flexible multivariate models. They, however, lose their flexibility with dimensions. Attempts have been existing to reduce the model complexity by searching for a subclass of truncation vine copulas, of which only a limited number of vine trees are estimated. However, they are either time-consuming or model-dependent or require additional computational efforts. Inspired by the relationship between copula’s parameters (and the corresponding Kendall’s tau) and the mutual information on the one side and the mutual information and copula entropy on another side, this study proposed a novel truncation vine copula model using only mutual information values among variables. This newly proposed truncation method is evaluated in simulation studies and a real application of financial returns dataset. The simulated and real studies show that the model is sufficiently good to find the most appropriate truncation level with a good fit of a given data.