Vine copula selection using mutual information for hydrological dependence modeling

Abstract

Hydrological risk analysis and management entails multivariate modeling which requires modeling the structure of dependence among different variables. Vine copulas have been increasing applied in multivariate modeling wherein the selection of vine copula structure plays a critical role. Inspired by the relationship between Mutual information (MI) and copula entropy (CE), this study discussed the connection between conditional mutual information (CMI) and CE and developed a mutual information-based sequential approach to select a vine structure which was based on original observations, and model-independent. Then, to reduce the complexity of R-vine copulas, a statistical method-based truncation procedure was applied. Finally, an MI-based approach for hydrological dependence modeling was developed. Two types of hydrological processes with different dependence structures were utilized to show the performance of the proposed approach: (i) drought characterization: showing a D-vine structure; and (ii) multi-site streamflow dependence: showing a C-vine structure. Results indicated that the MI-based approach satisfactorily modeled different kinds of dependence structure and yielded more information on variables in comparison with traditional tau-based approach.

Keywords: Conditional mutual information; Copula entropy; Hydrological dependence; Mutual information; Vine structure selection.