Asymmetric correlation matrices: an analysis of financial data

• Published in: The European physical journal. B, Condensed matter physics Condensed matter physics, 2012-06, Vol.85 (6), Article 213
• Main Authors: Livan, G., Rebecchi, L.
• Format: Article
• Language: English
• Subjects: Analysis; Applied sciences; Case studies; Complex Systems; Condensed Matter Physics; Exact sciences and technology; Financial markets; Fluid- and Aerodynamics; Operational research and scientific management; Operational research. Management science; Physics; Physics and Astronomy; Portfolio theory; Regular Article; Solid State Physics
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/e2012-30085-3

We analyse 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 matrix 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 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.