Dependence Measures

There exist several measures for the strength and direction of dependence between two random variables. The most common ones are the Pearson product–moment correlation, Kendall’s tau, and Spearman’s rho. We give a short introduction to these measures including their estimation based on data. Kendall’s tau and Spearman’s rho can be expressed in terms of the corresponding copula alone, while this is not always the case for the Pearson product–moment correlation. For joint extreme events, the notion of tail dependence coefficients will be introduced. Finally, the concepts of partial and conditional correlations will be discussed, which will play an important role in the class of multivariate vine copulas.