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Scaling and correlation in financial data

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  • Rama Cont

    (CEA Saclay & CNRS Nice)

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    Abstract

    The statistical properties of the increments x(t+T) - x(t) of a financial time series depend on the time resolution T on which the increments are considered. A non-parametric approach is used to study the scale dependence of the empirical distribution of the price increments x(t+T) - x(t) of S&P Index futures, for time scales T, ranging from a few minutes to a few days using high-frequency price data. We show that while the variance increases linearly with the timescale, the kurtosis exhibits anomalous scaling properties, indicating a departure from the iid hypothesis. Study of the dependence structure of the increments shows that although the autocorrelation function decays rapidly to zero in a few minutes, the correlation of their squares exhibits a slow power law decay with exponent 0.37, indicating persistence in the scale of fluctuations. We establish a link between the scaling behavior and the dependence structure of the increments : in particular, the anomalous scaling of kurtosis may be explained by "long memory" properties of the square of the increments.

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    File URL: http://arxiv.org/pdf/cond-mat/9705075
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number cond-mat/9705075.

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    Date of creation: May 1997
    Date of revision: May 1997
    Handle: RePEc:arx:papers:cond-mat/9705075

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    Web page: http://arxiv.org/

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    References

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    1. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
    2. Marc Potters & Rama Cont & Jean-Philippe Bouchaud, 1996. "Financial markets as adaptative systems," Science & Finance (CFM) working paper archive 500037, Science & Finance, Capital Fund Management.
    3. Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
    4. Rama Cont & Marc Potters & Jean-Philippe Bouchaud, 1997. "Scaling in stock market data: stable laws and beyond," Papers cond-mat/9705087, arXiv.org.
    5. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
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    Cited by:
    1. Huber, Jürgen & Kleinlercher, Daniel & Kirchler, Michael, 2012. "The impact of a financial transaction tax on stylized facts of price returns—Evidence from the lab," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1248-1266.
    2. Kirchler, Michael & Huber, Jurgen, 2007. "Fat tails and volatility clustering in experimental asset markets," Journal of Economic Dynamics and Control, Elsevier, vol. 31(6), pages 1844-1874, June.

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