Quantifying and interpreting collective behavior in financial markets.

Firms having similar business activities are correlated. We analyze two different cross-correlation matrices C constructed from (i) 30-min price fluctuations of 1000 US stocks for the two-year period 1994-95 and (ii) one-day price fluctuations of 422 US stocks for the 35-year period 1962-96. We find that the eigenvectors of C corresponding to the largest eigenvalues allow us to partition the set of all stocks into distinct subsets. These subsets are similar to business sectors, and are stable for extended periods of time. We find that price fluctuations of these subsets are characterized by power-law decaying time correlations, reminiscent of strongly interacting systems.