Arthur Charpentier (see Arthur’s blog) was recently contacted by some researchers willing to test if a multivariate copula is or not Gaussian. They use a test proposed in Malevergne and Sornette (2003) stating that one should simply test for pairwise normality. This test may be of importance in finance, in actuarial science, and in risk management in general: for example, given 120 financial as...

Copula modelling has become ubiquitous in modern statistics. Here, the problem of nonparametrically estimating a copula density is addressed. Arguably the most popular nonparametric density estimator, the kernel estimator is not suitable for the unit-square-supported copula densities, mainly because it is heavily a↵ected by boundary bias issues. In addition, most common copulas admit unbounded ...

The study of dependence between random variables is a mainstay in statistics. In many cases, the strength of dependence between two or more random variables varies according to the values of a measured covariate. We propose inference for this type of variation using a conditional copula model where the copula function belongs to a parametric copula family and the copula parameter varies with th...

We discuss the connection between information and copula theories by showing that a copula can be employed to decompose the information content of a multivariate distribution into marginal and dependence components, with the latter quantified by the mutual information. We define the information excess as a measure of deviation from a maximum entropy distribution. The idea of marginal invariant ...

Across the animal kingdom the duration of copulation varies enormously from a few seconds to several days. Functional explanations for this variation are largely embedded within sperm competition theory in which males modulate the duration of copula in order to optimize their fitness. However, copulation is the union of two protagonists which are likely to have separate and often conflicting re...

Article history: Received 12 July 2010 Received in revised form 5 May 2011 Accepted 12 May 2011 Available online 18 May 2011 Traditional credit risk models adopt the linear correlation as a measure of dependence and assume that credit losses are normally-distributed. However some studies have shown that credit losses are seldom normal and the linear correlation does not give accurate assessment...

The theory of conditional copulas provides a means of constructing °exible multivariate density models, allowing for time-varying conditional densities of each individual variable, and for timevarying conditional dependence between the variables. Further, the use of copulas in constructing these models often allows for the partitioning of the parameter vector into elements relating only to a ma...

The estimation of dependencies between multiple variables is a central problem in the analysis of financial time series. A common approach is to express these dependencies in terms of a copula function. Typically the copula function is assumed to be constant but this may be inaccurate when there are covariates that could have a large influence on the dependence structure of the data. To account...

The paper deals with modeling of mutual dependencies among financial assets. Its aim is to investigate the impact of different copula assumptions on optimal portfolios, when CVaR optimization is used. Strategic asset allocation perspective is supposed. It is demonstrated that copula functions enable us to separate the modeling of dependency features of financial assets from the modeling of marg...

In this paper, we seek to examine the effect of the presence of long memory on the dependence structure between financial returns and on portfolio optimization. First, we focus on the dependence structure using copulas. To select the best copula, in addition to the goodness of fit tests, we employ a graphical method based on visual comparison of the fitted copula density and the smoothed copula...