Non-linear correlation analysis in financial markets using hierarchical clustering

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.

COVID anomaly in the correlation analysis of S&P 500 market states

“…PR takes values between 1 and N and for a Gaussian Orthogonal Ensemble (GOE) has the limiting value of N/3 [29][30][31]. This GOE result holds true for correlation matrices as well and will be seen in the center of the spectrum for sufficiently long epochs.…”

“…Participation ratios (PR) gives the number of components that participate significantly in each eigenvector v , PR takes values between 1 and N and for a Gaussian Orthogonal Ensemble (GOE) has the limiting value of N /3 [ 29 – 31 ]. This GOE result holds true for correlation matrices as well and will be seen in the center of the spectrum for sufficiently long epochs.…”