Luís A. Nunes Amaral

co-Director, Northwestern Institute on Complex Systems
Professor of Chemical & Biological Engineering
Professor of Physics & Astronomy (by courtesy)
Professor of Medicine (by courtesy)

Chemical & Biological Engineering
2145 Sheridan Road (Room E136)
Evanston, IL 60208, US
Phone: (847) 491-7850

Universal and nonuniversal properties of cross correlations in financial time series

Plerou V, Gopikrishnan P, Rosenow B, Amaral LAN, Stanley HE
Physical Review Letters 83, 1471-1474 (1999)
Times cited: 548

Abstract

We use methods of random matrix theory to analyze the cross-correlation matrix 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 C agree with the predictions of random matrix theory, but there are deviations for a few of the largest eigenvalues. We find that C has the universal properties of the Gaussian orthogonal ensemble of random matrices. Furthermore, we analyze the eigenvectors of 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.