Nonparametric Finance

Chapter 4Multivariate Data Analysis

Multivariate data analysis studies simultaneously several time series, but the time series properties are ignored, and thus the analysis can be called cross-sectional.

The copula is an important concept of multivariate data analysis. Copula models are a convenient way to separate multivariate analysis to the purely univariate and to the purely multivariate components. We compose a multivariate distribution into the part that describes the dependence and into the parts that describe the marginal distributions. The marginal distributions can be estimated efficiently using nonparametric methods, but it can be useful to apply parametric models to estimate dependence, for a high-dimensional distribution. Combining nonparametric estimators of marginals and a parametric estimator of the copula leads to a semiparametric estimator of the distribution.

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, because they are determined by the copula, whereas linear correlation is affected by marginal distributions. Coefficients of tail dependence can capture whether the dependence of asset returns is larger during the periods of high volatility.

Multivariate graphical tools include scatter plots, which can be combined with multidimensional ...