Statistical Measures of Dependence for Financial Data

This chapter provides the statistical measures of dependence for financial data. The analysis of financial and econometric data is typified by non-Gaussian multivariate observations that exhibit complex dependencies: heavy-tailed and skewed marginal distributions are commonly encountered; serial dependence, such as autocorrelation and conditional heteroscedasticity. When data are assumed to be jointly Gaussian, all dependence is linear, and therefore only pairwise among the variables. In this setting, Pearson's product-moment correlation coefficient uniquely characterizes the sign and strength of any such dependence. The chapter shows that copulas can be used to model the dependence between random variables. It turns our attention to the dependence structure itself, and when appropriate makes connections to copulas. The chapter describes different types of dependence, and then provides theoretical background.