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Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series

Vasiliki Plerou, Parameswaran Gopikrishnan, Bernd Rosenow, Luís A. Nunes Amaral, and H. Eugene Stanley
Phys. Rev. Lett. 83, 1471 – Published 16 August 1999
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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.

  • Received 22 February 1999

DOI:https://doi.org/10.1103/PhysRevLett.83.1471

©1999 American Physical Society

Authors & Affiliations

Vasiliki Plerou1,2, Parameswaran Gopikrishnan1, Bernd Rosenow3, Luís A. Nunes Amaral1, and H. Eugene Stanley1

  • 1Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215
  • 2Department of Physics, Boston College, Chestnut Hill, Massachusetts 02167
  • 3Institut für Theoretische Physik, Universität zu Köln, D-50937 Köln, Germany

See Also

The Market Isn’t All Random

Phys. Rev. Focus 4, 10 (1999)

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Issue

Vol. 83, Iss. 7 — 16 August 1999

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