Correlations in Economic Time Series

Abstract

The correlation function of a financial index of the New York stock exchange, the S&P 500, is analyzed at 1 min intervals over the 13-year period, Jan 84 -- Dec 96. We quantify the correlations of the absolute values of the index increment. We find that these correlations can be described by two different power laws with a crossover time t_\times\approx 600 min. Detrended fluctuation analysis gives exponents $\hat{I}{\pm }_1=0.66$ and $\hat{I}{\pm }_2=0.93$ for $t<t_{\times }$ and $t>t_{\times }$ respectively. Power spectrum analysis gives corresponding exponents ${\hat{I}}_1^2=0.31$ and ${\hat{I}}_2^2=0.90$ for $f>f_{\times }$ and $f<f_{\times }$ respectively.

6 pages, 2 figures