Correlations in Economic Time Series

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 $α_1=0.66$ and $α_2=0.93$ for $t<t_\times$ and $t>t_\times$ respectively. Power spectrum analysis gives corresponding exponents $β_1=0.31$ and $β_2=0.90$ for $f>f_\times$ and $f< f_\times$ respectively.

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