A Mixture of Regular Vines for Multiple Dependencies

Fadhah Amer Alanazi

doi:10.1155/2021/5559518

Abstract

To uncover complex hidden dependency structures among variables, researchers have used a mixture of vine copula constructions. To date, these have been limited to a subclass of regular vine models, the so-called drawable vine, fitting only one type of bivariate copula for all variable pairs. However, the variation of complex hidden correlations from one pair of variables to another is more likely to be present in many real datasets. Single-type bivariate copulas are unable to deal with such a problem. In addition, the regular vine copula model is much more capable and flexible than its subclasses. Hence, to fully uncover and describe complex hidden dependency structures among variables and provide even further flexibility to the mixture of regular vine models, a mixture of regular vine models, with a mixed choice of bivariate copulas, is proposed in this paper. The model was applied to simulated and real data to illustrate its performance. The proposed model shows significant performance over the mixture of R-vine densities with a single copula family fitted to all pairs.

Highlights

Real data often exhibit complex multivariate mixture dependency structures among variables. ese dependencies may vary from one pair of variables to another. e variation in the dependency structures adds extra complexity for modelling and capturing these types of relationships. e Gaussian mixture model is commonly used to model data with complex dependency structures due to its ease of implementation
Erefore, inspired by and building on the works of Dißmann et al [17] and Kim et al [12], this paper develops the first mixture of the regular vine (R-vine) density model, with a mixed choice of bivariate copulas, in the literature. e new proposed model aims to introduce higher flexibility to mixture vine copula models, providing a way to fully captured mixed hidden complex correlations among variables
Since the primary focus of this paper is to introduce a new mixture model, the types of bivariate copula families used in the simulation studies are prespecified as the most commonly used copula families

Summary

Introduction

Real data often exhibit complex multivariate mixture dependency structures among variables. ese dependencies may vary from one pair of variables to another. e variation in the dependency structures adds extra complexity for modelling and capturing these types of relationships. e Gaussian mixture model is commonly used to model data with complex dependency structures due to its ease of implementation. A mixture of D-vine copulas was introduced by Zheng et al [13] for chemical process monitoring In their models, only one type of copula family was fitted to all pairs of variables. Erefore, inspired by and building on the works of Dißmann et al [17] and Kim et al [12], this paper develops the first mixture of the R-vine density model, with a mixed choice of bivariate copulas (copula family is specified individually for each pair in each density), in the literature. E new proposed model aims to introduce higher flexibility to mixture vine copula models, providing a way to fully captured mixed hidden complex correlations among variables. The new mixture model is compared with a mixture R-vine model where a single copula family is fitted to all pairs of the variables

Theoretical Background

A Mixture of R-Vine Densities

Simulated Data Application

Real Data Application

Conclusion