Financial Time Series: A Physics Perspective

Physicists in the last few years have started applying concepts and methods of statistical physics to understand economic phenomena. The word "econophysics" is sometimes used to refer to this work. One reason for this interest is the fact that Economic systems such as financial markets are examples of complex interacting systems for which a huge amount of data exist and it is possible that economic problems viewed from a different perspective might yield new results. This article reviews the results of a few recent phenomenological studies focussed on understanding the distinctive statistical properties of financial time series. We discuss three recent results — (i) The probability distribution of stock price fluctuations: Stock price fluctuations occur in all magnitudes, in analogy to earthquakes — from tiny fluctuations to very drastic events, such as market crashes, eg., the crash of October 19th 1987, sometimes referred to as " Black Monday". The distribution of price fluctuations decays with a power-law tail well outside the Levy stable regime and describes fluctuations that differ by as much as 8 orders of magnitude. In addition, this distribution preserves its functional form for fluctuations on time scales that differ by 3 orders of magnitude, from 1 min up to approximately 10 days, (ii) Correlations in financial time series: While price fluctuations themselves have rapidly decaying correlations, the magnitude of fluctuations measured by either the absolute value or the square of the price fluctuations has correlations that decay as a power-law and persist for several months, (iii) Correlations among different companies: The third result bears on the application of random matrix theory to understand the correlations among price fluctuations of any two different stocks. Prom a study of the eigenvalue statistics of the cross-correlation matrix constructed from price fluctuations of the leading 1000 stocks, we find that the largest 5-10% of the eigenvalues and the corresponding eigenvectors show systematic deviations from the predictions for a random matrix, whereas the rest of the eigenvalues conform to random matrix behavior — suggesting that these 5-10% of the eigenvalues contain system-specific information about correlated behavior. The Center for Polymer Studies is supported by the National Science Foundation. CP519, Statistical Physics, edited by M. Tokuyama and H. E. Stanley © 2000 American Institute of Physics l-56396-940-8/00/$17.00