Non-linear correlation analysis in financial markets using hierarchical clustering

TL;DR

This paper employs the distance correlation coefficient to detect nonlinear associations in financial markets, using hierarchical clustering to analyze stock relationships in the S&P 500, revealing complex market dynamics.

Contribution

It introduces the application of the distance correlation coefficient combined with hierarchical clustering to analyze nonlinear relationships in financial data.

Findings

Identification of nonlinear correlations among stocks

Hierarchical clustering reveals market state evolution

Enhanced understanding of financial market dynamics

Abstract

Distance correlation coefficient (DCC) can be used to identify new associations and correlations between multiple variables. The distance correlation coefficient applies to variables of any dimension, can be used to determine smaller sets of variables that provide equivalent information, is zero only when variables are independent, and is capable of detecting nonlinear associations that are undetectable by the classical Pearson correlation coefficient (PCC). Hence, DCC provides more information than the PCC. We analyze numerous pairs of stocks in S\&P500 database with the distance correlation coefficient and provide an overview of stochastic evolution of financial market states based on these correlation measures obtained using agglomerative clustering.