Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series

We use methods of random matrix theory to analyze the cross-correlation matrix $\mathbf{C}$ of stock price changes of the largest 1000 U.S. companies for the 2-year period 1994–1995. We find that the statistics of most of the eigenvalues in the spectrum of $\mathbf{C}$ agree with the predictions of random matrix theory, but there are deviations for a few of the largest eigenvalues. We find that $\mathbf{C}$ has the universal properties of the Gaussian orthogonal ensemble of random matrices. Furthermore, we analyze the eigenvectors of $\mathbf{C}$ through their inverse participation ratio and find eigenvectors with large ratios at both edges of the eigenvalue spectrum—a situation reminiscent of localization theory results.