  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 dependence measures is also discussed and used to show that
empirical linear correlation underestimates the amplitude of the actual
correlation in the case of non-Gaussian marginals. The mutual information is
shown to provide an upper bound for the asymptotic empirical log-likelihood of
a copula. An analytical expression for the information excess of T-copulas is
provided, allowing for simple model identification within this family. We
illustrate the framework in a financial data set.
