Multivariate Data Analysis

Abstract

Copula models are a convenient way to separate multivariate data analysis to the purely univariate and to the purely multivariate components. Multivariate data can be described using such statistics as linear correlation, Spearman's rank correlation, and Kendall's rank correlation. Linear correlation is used in the Markowitz portfolio selection. Rank correlations are more natural concepts to describe dependence. Coefficients of tail dependence can capture whether the dependence of asset returns is larger during the periods of high volatility. This chapter studies measures of dependence and considers multivariate graphical tools. Multivariate graphical tools include scatter plots, which can be combined with multidimensional scaling and other dimension reduction methods. The chapter defines multivariate parametric distributions such as multivariate normal, multivariate Student, and elliptical distributions. It provides examples of multivariate parametric models. The examples include Gaussian and Student distributions. The chapter also provides examples of parametric families of copulas. The examples include the Gaussian copulas and the Student copulas.