Asymmetric matrices in an analysis of financial correlations

TL;DR

This paper explores the use of asymmetric correlation matrices with complex eigenspectra, derived from Random Matrix Theory, to analyze delayed dependencies and temporal structures in financial market correlations, revealing near-simultaneous evolution of US and German markets.

Contribution

It introduces the application of asymmetric correlation matrices with complex eigenvalues to empirical financial data, highlighting their ability to detect subtle temporal dependencies.

Findings

US and German markets evolve almost simultaneously

Only a subtle indication of German market leading US by seconds

Asymmetric matrices reveal temporal correlation structures

Abstract

Financial markets are highly correlated systems that reveal both the inter-market dependencies and the correlations among their different components. Standard analyzing techniques include correlation coefficients for pairs of signals and correlation matrices for rich multivariate data. In the latter case one constructs a real symmetric matrix with real non-negative eigenvalues describing the correlation structure of the data. However, if one performs a correlation-function-like analysis of multivariate data, when a stress is put on investigation of delayed dependencies among different types of signals, one can calculate an asymmetric correlation matrix with complex eigenspectrum. From the Random Matrix Theory point of view this kind of matrices is closely related to Ginibre Orthogonal Ensemble (GinOE). We present an example of practical application of such matrices in correlation analyses of empirical data. By introducing the time lag, we are able to identify temporal structure of the inter-market correlations. Our results show that the American and German stock markets evolve almost simultaneously without a significant time lag so that it is hard to find imprints of information transfer between these markets. There is only an extremely subtle indication that the German market advances the American one by a few seconds.