Thurner, S.,Biely, C.
We derive the exact form of the eigenvalue spectrum of correlation matrices obtained from a set of N time-shifted, iid Gaussian time-series of length T. These matrices are random, real and asymmetric matrices with a superimposed structure due to the time-lag. We demonstrate that the associated (complex) eigenvalue spectrum is circular symmetric for large matrices (lim N -> infinity). This fact allows to exactly compute the eigenvalue density via the inverse Abel-transform of the density of the symmetrized problem. The validity of the approach is demonstrated by comparison to numerical realizations of random time-series. As an example, spectra of correlation matrices from time-lagged financial data are presented.