Fluctuations and Their Correlations in Econophysics

Abst rac t. We address a current question in econophysics: Are fluctuations in eco-nomic indices correlated? To this end, we analyze 1-minute data on a stock index, the Standard and Poor index of the 500 largest stocks. We extend the 6-year data base studied by Mantegna and Stanley by including the 13 years 1984-1996 inclu-sive, with a recording frequency of 15 seconds. The total number of data points in this 13 years period exceed 4.5 million, which allows for a very detailed statistical analysis. We find that the fluctuations in the volatility are correlated, and that the correlations are well described by a power law. 1 I n t r o d u c t i o n Today we are going to look at some examples of scale-invariant correlations that are of interest to social scientists. At one time, it was imagined that the "scale-free " phenomena are rel-evant to only a fairly narrow slice of physical phenomena (Stanley 1971). However, the range of systems that apparently display power law and hence scale-invariant correlations has increased dramatically in recent years, rang-ing from base pair correlations in noncoding DNA (Pent et al. 1992, Arneod