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Hidden temporal order unveiled in stock market volatility variance

Yoash Shapira, Dror Y. Kenett, Ohad Raviv, Eshel ben-Jacob

posted on 28 May 2011

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Time series of the daily return of financial indices are some of the best examples for the output of Complex Adaptive Systems (CAS). It is usually accepted that the these time series are random. We have found that the correlation between the variances and means of segments of these time series is very large and thus cannot be the output of random series, unless it has some temporal order in it. Trying to quantify this temporal order, we could not find it in the series of the daily return, but rather in the volatility, which is the variation of these time series. We found that the behavior of the shuffled time series is equivalent to that of a random time series, while that of the original time series have large deviations from the expected random behavior, which is the result of temporal structure.