Econophysics: financial time series from a statistical physics point of view

In recent years, physicists have started applying concepts and methods of s tatistical physics to study economic problems. The word "Econophysics" is s ometimes used to refer to this work. Much recent work is focused on underst anding the statistical properties of financial time series. One reason for this interest is that financial markets are examples of complex interacting systems for which a huge amount of data exist and it is possible that fina ncial time series viewed from a different perspective might yield new resul ts. This article reviews the results of three recent phenomenological studi es - (i) The probability distribution of stock price fluctuations. Stock pr ice fluctuations occur in all magnitudes, in analogy to earthquakes - from tiny fluctuations to drastic events, such as market crashes. The distributi on of price fluctuations decays with a power-law tail well outside the Levy stable regime and describes fluctuations that differ by as much as eight o rders of magnitude. In addition, this distribution preserves its functional form for fluctuations on time scales that differ by three orders of magnit ude, fi om I min up to approximately 10 d. (ii) Correlations in financial t ime series: While price fluctuations themselves have rapidly decaying corre lations, the magnitude of fluctuations measured by either the absolute valu e or the square of the price fluctuations has correlations that decay as a power-law and persist for several months. (iii) Correlations among differen t companies: The third result bears on the application of random matrix the ory to understand the correlations among price fluctuations of any two diff erent stocks. From a study of the eigenvalue statistics of the cross-correl ation matrix constructed from price fluctuations of the leading 1000 stocks , we find that the largest approximate to 1% of the eigenvalues and the cor responding eigenvectors show systematic deviations from the predictions for a random matrix, whereas the rest of the eigenvalues conform to random mat rix behavior - suggesting that these 1% of the eigenvalues contain system-s pecific information about correlated time evolution of different companies. (C) 2000 Published by Elsevier Science B.V. All rights reserved.