K. Choi and O. Kum (USA)
time series analysis, S&P 500 daily index, chaotic behavior, correlation exponent, phase-space reconstruction,strange attractors
We have investigated the existence of chaotic behavior in the 51 years S&P 500 daily indices using correlation ex ponent analysis. 12920 data points of S&P daily indices from 19 January 1950 to 19 January 2001 were used. In this paper we focused on finding out the minimum and suf ficient number of variables to model the dynamics. As a basis for discriminating chaotic and stochastic behaviors, we used the correlation dimension. The calculation of the delay time for the phase-space reconstruction was done by trial and error method. The results show positive evidence of the existence of chaotic behavior in the long time S&P 500 daily indices. The minimum number of variables es sential to model the dynamics was identified to be three while the number of variables sufficient to model the dy namics was about 160 for the long time S&P daily indices. The number of data points of 51 years S&P daily indices were sufficient enough to compute the correlation dimen sion.
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