Regensburg 2007 – scientific programme
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AKSOE: Arbeitskreis Physik sozio-ökonomischer Systeme
AKSOE 14: Financial Markets and Risk Management III
AKSOE 14.7: Talk
Thursday, March 29, 2007, 17:15–17:45, H8
Theoretical predictions and empirical observations of eigenvalue spectra of time-lagged correlation matrices — •Christoly Biely1,2 and Stefan Thurner1,2 — 1Complex Systems Research Group, HNO, Medical University of Vienna, Währinger Gürtel 18-20, A-1090 Vienna, Austria — 2Atominstitut d. österr. Universitäten, Stadionallee 2, A-1020 Vienna, Austria
Recently, the study of eigenvalue spectra of financial correlation matrices has attracted considerable interest due to its applications in financial engineering. We contribute a theoretical understanding of the case of time-lagged correlation matrices, which can be seen as real, asymmetric matrices with a special structure superimposed due to the shifting of the individual time-series: We prove that the respective eigenvalue spectra are circular symmetric in the complex plane under the assumption of time-series being (finite) Brownian random walks. Further, we solve the problem of determining their radial eigenvalue density via an inverse Abel-Transform of the solution of the eigenvalue density of the symmetrized problem. We then compare the theoretical results with empirical 5 minute returns of the S&P500 and discuss the observed deviations. Non-trivial patterns such as 'causal industry sectors' and non-random structures indicated by eigenvalues departing from the theoretical spectrum are discussed in some detail.