Correlations in economic time series

A financial index of the New York stock exchange, the S&P500, is analyzed at 1 min intervals over the 13 yr period, January 84–December 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 tx 600 min. Detrended fluctuation analysis gives exponents α1 = 0.66 and α2 = 0.93 for t < tx and t> tx, respectively. Power spectrum analysis gives corresponding exponents β1 = 0.31 and β2 = 0.90 for f> fx and f < fx, respectively.