As multivariate distributions with uniform one-dimensional margins, copulas provide very convenient models for studying dependence structure with tools that are scale-free. Each copula (n-copula) represents the whole class of continuous bivariate (multivariate) distributions from which it has been obtained when one-dimensional marginals were transformed by their cdf’s. The similar property, how...

We propose the ‘Copula PC’ algorithm for causal discovery from a combination of continuous and discrete data, assumed to be drawn from a Gaussian copula model. It is based on a two-step approach. The first step applies Gibbs sampling on rank-based data to obtain samples of correlation matrices. These are then translated into an average correlation matrix and an effective number of data points, ...

We propose a new method for a nonparametric estimation of Rényi and Shannon information for a multivariate distribution using a corresponding copula, a multivariate distribution over normalized ranks of the data. As the information of the distribution is the same as the negative entropy of its copula, our method estimates this information by solving a Euclidean graph optimization problem on the...

In this paper we provide three nonparametric tests of independence between continuous random variables based on Bernstein copula and copula density. The first test is constructed based on functional of Cramér-von Mises of the Bernstein empirical copula. The two other tests are based on Bernstein density copula and use Cramér-von Mises and Kullback-Leiber divergencetype respectively. Furthermore...

This paper introduces copula functions and the use of the Gaussian copula function to model probabilistic dependencies in supervised classification tasks. A copula is a distribution function with the implicit capacity to model non linear dependencies via concordance measures, such as Kendall’s τ . Hence, this work studies the performance of a simple probabilistic classifier based on the Gaussia...

By a theorem due to Sklar, a multivariate distribution can be represented in terms of its underlying margins by binding them together using a copula function. By exploiting this representation, the “copula approach” to modelling proceeds by specifying distributions for each margin, and a copula function. In this article, a number of copula functions are given, with attention focusing on members...

Copulas offer economic agents facing uncertainty a powerful and flexible tool to model dependence between random variables and are preferable to the traditional, correlation-based approach. In this paper we show how standard tests for the fit of a distribution can be extended to copulas. Because they can be applied to any copula and because they are based on a direct comparison of a given copul...

This paper develops a method for pricing bivariate contingent claims under General Autoregressive Conditionally Heteroskedastic (GARCH) process. As the association between the underlying assets may vary over time, the dynamic copula with time-varying parameter offers a better alternative to any static model for dependence structure and even to the dynamic copula model determined by dynamic depe...

Besides their advantage in modelling tail-dependency, the main drawback of standard non-Gaussian copula is the homogeneity in the tail dependency parameter. Several approaches to solve this are meanwhile developed, hierachical copula, the grouped t-copula and the heterogeneous t-copula as recently described by Luo and Shevchenko [1]. We will show results from a concrete implementation of a fact...

This paper concerns the application of copula functions in VaR valuation. The copula function is used to model the dependence structure of multivariate assets. After the introduction of the traditional Monte Carlo simulation method and the pure copula method we present a new algorithm based on mixture copula functions and the dependence measure, Spearman’s rho. This new method is used to simula...