Summary: Fluctuations and Their Correlations
Y. Liu, L.A.N. Amaral, P. Cizeau, P. Gopikrishnan,
M. Meyer, C.-K. Peng and H.E. Stanley
Center for Polymer Studies and Department of Physics
Boston University, Boston, MA 02215, USA
Abstract. 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.
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