Asymmetric correlation matrices: an analysis of financial data

TL;DR

This paper investigates the spectral properties of asymmetric correlation matrices in financial data, revealing non-trivial correlations between markets and time-lagged effects through advanced random matrix theory analysis.

Contribution

It extends spectral analysis to non symmetric matrices in finance, using random matrix theory to identify meaningful correlations between markets and their principal components.

Findings

Detected non trivial correlations between American and British stock markets.

Identified significant time-lagged correlations in financial data.

Validated findings with asymmetric correlation matrices of principal components.

Abstract

We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson correlation matrices to the realm of complex eigenvalues. We employ some recent random matrix theory results on the average eigenvalue density of this type of matrices to distinguish between noise and non trivial correlation structures, and we focus on financial data as a case study. Namely, we employ daily prices of stocks belonging to the American and British stock exchanges, and look for the emergence of correlations between two such markets in the eigenvalue spectrum of their non symmetric correlation matrix. We find several non trivial results, also when considering time-lagged correlations over short lags, and we corroborate our findings by additionally studying the asymmetric correlation matrix of the principal components of our datasets.