## Abstract

We review recent work on quantifying collective behavior among stocks by applying the conceptual framework of random matrix theory (RMT), developed in physics to describe the energy levels of complex systems. RMT makes predictions for "universal" properties that do not depend on the interactions between the elements comprising the system; deviations from RMT provide clues regarding system-specific properties. We compare the statistics of the cross-correlation matrix C - whose elements C_{ij} are the correlation coefficients of price fluctuations of stock i and j - against a random matrix having the same symmetry properties. It is found that RMT methods can distinguish random and non-random parts of C. The non-random part of C which deviates from RMT results, provides information regarding genuine collective behavior among stocks.

Original language | English (US) |
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Pages (from-to) | 175-180 |

Number of pages | 6 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 299 |

Issue number | 1-2 |

DOIs | |

State | Published - Oct 1 2001 |

Event | Application of Physics in Economic Modelling (NATO ARW) - Prague, Czech Republic Duration: Feb 8 2001 → Feb 10 2001 |

## Keywords

- Collective phenomena
- Financial time series
- Random matrix theory

## ASJC Scopus subject areas

- Statistics and Probability
- Condensed Matter Physics