Random matrix ensembles of time-lagged correlation matrices: Derivation of eigenvalue spectra and analysis of financial time-series

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dc.creatorBiely, Christoly
dc.creatorThurner, Stefan
dc.date2006-09-07
dc.date.accessioned2026-07-07T12:07:51Z
dc.date.available2026-07-07T12:07:51Z
dc.descriptionWe derive the exact form of the eigenvalue spectra of correlation matrices derived from a set of time-shifted, finite Brownian random walks (time-series). These matrices can be seen as random, real, asymmetric matrices with a special structure superimposed due to the time-shift. We demonstrate that the associated eigenvalue spectrum is circular symmetric in the complex plane for large matrices. This fact allows us to exactly compute the eigenvalue density via an inverse Abel-transform of the density of the symmetrized problem. We demonstrate the validity of this approach by numerically computing eigenvalue spectra of lagged correlation matrices based on uncorrelated, Gaussian distributed time-series. We then compare our theoretical findings with eigenvalue densities obtained from actual high frequency (5 min) data of the S&P500 and discuss the observed deviations. We identify various non-trivial, non-random patterns and find asymmetric dependencies associated with eigenvalues departing strongly from the Gaussian prediction in the imaginary part. For the same time-series, with the market contribution removed, we observe strong clustering of stocks, i.e. causal sectors. We finally comment on the time-stability of the observed patterns.
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/physics/0609053
dc.identifierhttp://arxiv.org/abs/physics/0609053
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/209118
dc.subjectPhysics and Society
dc.subjectStatistical Finance
dc.titleRandom matrix ensembles of time-lagged correlation matrices: Derivation of eigenvalue spectra and analysis of financial time-series
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