We propose two new principal component analysis methods in this paper utilizing a semiparametric model. The according methods are named Copula Component Analysis (COCA) and Copula PCA. The semiparametric model assumes that, after unspecified marginally monotone transformations, the distributions are multivariate Gaussian. The COCA and Copula PCA accordingly estimate the leading eigenvectors of ...

This paper provides a new approach to recover relative entropy measures of contemporaneous dependence from limited information by constructing the most entropic copula (MEC) and its canonical form, namely the most entropic canonical copula (MECC). The MECC can effectively be obtained by maximizing Shannon entropy to yield a proper copula such that known dependence structures of data (e.g., meas...

In recent years, the use of copulas has grown extremely fast and with it, the need for a simple and reliable method to choose the right copula family. Existing methods pose numerous difficulties and none is entirely satisfactory.We propose a Bayesian method to select the most probable copula family among a given set. The copula parameters are treated as nuisance variables, and hence do not have...

We analyze the statistical dependence structure of the S&P 500 constituents in the 4-year period from 2007 to 2010 using intraday data from the New York Stock Exchange’s TAQ database. Instead of using a given parametric copulawith a predetermined shape, we study the empirical pairwise copula directly. We find that the shape of this copula resembles the Gaussian copula to somedegree, but exhibit...

The empirical copula process plays a central role for statistical inference on copulas. Recently, Segers (2012) investigated the asymptotic behavior of this process under non-restrictive smoothness assumptions for the case of i.i.d. random variables. In the first part of the talk, we extend his main result to the case of serial dependent random variables by means of the powerful and elegant fun...

In recent years, copulas have become very popular in financial research and actuarial science as they are more flexible in modelling the co-movements and relationships of risk factors as compared to the conventional linear correlation coefficient by Pearson. However, a precise estimation of the copula parameters is vital in order to correctly capture the (possibly nonlinear) dependence structur...

Consider semiparametric bivariate copula models in which the family of copula functions is parametrized by a Euclidean parameter of interest and in which the two unknown marginal distributions are the (innnite dimensional) nuisance parameters. The eecient score for can be characterized in terms of the solutions of two coupled Sturm-Liouville equations. In case the family of copula functions cor...

The valuation of basket default swaps depends crucially on the joint default probability of the underlying assets in the basket. It is known that this probability can be modeled by means of a copula function which links the marginal default probabilities to a joint probability. The valuation bears risk due to the uncertainty of the copula, the relation of the assets to each other and the margin...

We introduce a dimension reduction technique based on extreme observations. The classical assumption of a linear model for the distribution of a random vector is replaced by the weaker assumption of a fairly general model for the copula. We assume an elliptical copula to describe the extreme dependence structure, which preserves a ’correlation-like’ structure in the extremes. Based on the tail ...

We introduce a general approach to nonlinear quantile regression modelling that is based on the specification of the copula function that defines the dependency structure between the variables of interest. Hence we extend Koenker and Bassett’s [1978] original statement of the quantile regression problem by determining a distribution for the dependent variable Y conditional on the regressors X a...