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We analyze the spectral properties of correlation matrices between distinctstatistical systems. Such matrices are intrinsically non symmetric, and lendthemselves to extend the spectral analyses usually performed on standardPearson correlation matrices to the realm of complex eigenvalues. We employsome recent random matrix theory results on the average eigenvalue density ofthis type of matrices to distinguish between noise and non trivial correlationstructures, and we focus on financial data as a case study. Namely, we employdaily prices of stocks belonging to the American and British stock exchanges,and look for the emergence of correlations between two such markets in theeigenvalue spectrum of their non symmetric correlation matrix. We find severalnon trivial results, also when considering time-lagged correlations over shortlags, and we corroborate our findings by additionally studying the asymmetriccorrelation matrix of the principal components of our datasets.

Asymmetric correlation matrices: an analysis of financial data