Nonparametric dependence modeling via cluster analysis : a financial contagion application.

Abstract

Dependence measures, from linear correlation coefficients to recent copula-based methods, have been widely used to find out associations between variables. Although the latter type of measure has overcome many drawbacks of traditional measures, copula has intrinsically some undesirable characteristics for particular applications. In this paper, we discuss dependence modeling from a pattern recognition perspective and then introduce a new non-parametric approach based on anomaly detection through cluster analysis. The proposed methodology uses a weighting procedure based on Voronoi cells densities, named Weighted Voronoi Distance (WVD), to identify potentially atypical associations between univariate time series. The advantages are two-fold. First, the time series structure is respected and neither independence nor homoscedasticity is presumed within data. Second, any distribution of the data and any dependence function is allowed. An inference procedure is presented and simulation studies help to visualize the behavior and benefits of the proposed measure. Finally, real financial data is used to analyze the detection capacity of the contagion effect in financial markets during the 2007 sub-prime crisis. Different asset classes were included, and the WVD was able to signalize anomalies more strongly than the Extreme Value Theory and copula approach.