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Multifractality in the stock market: price increments versus waiting times

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  • Oświe¸cimka, P.
  • Kwapień, J.
  • Drożdż, S.
Abstract
By applying the multifractal detrended fluctuation analysis to the high-frequency tick-by-tick data from Deutsche Börse both in the price and in the time domains, we investigate multifractal properties of the time series of logarithmic price increments and inter-trade intervals of time. We show that both quantities reveal multiscaling and that this result holds across different stocks. The origin of the multifractal character of the corresponding dynamics is, among others, the long-range correlations in price increments and in inter-trade time intervals as well as the non-Gaussian distributions of the fluctuations. Since the transaction-to-transaction price increments do not strongly depend on or are almost independent of the inter-trade waiting times, both can be sources of the observed multifractal behaviour of the fixed-delay returns and volatility. The results presented also allow one to evaluate the applicability of the Multifractal Model of Asset Returns in the case of tick-by-tick data.

Suggested Citation

  • Oświe¸cimka, P. & Kwapień, J. & Drożdż, S., 2005. "Multifractality in the stock market: price increments versus waiting times," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 347(C), pages 626-638.
    • Handle: RePEc:eee:phsmap:v:347:y:2005:i:c:p:626-638
    DOI: 10.1016/j.physa.2004.08.025
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    References listed on IDEAS

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    1. Thomas Lux, 2003. "The Multi-Fractal Model of Asset Returns:Its Estimation via GMM and Its Use for Volatility Forecasting," Computing in Economics and Finance 2003 14, Society for Computational Economics.
    2. Laurent Calvet & Adlai Fisher & Benoit Mandelbrot, 1997. "Large Deviations and the Distribution of Price Changes," Cowles Foundation Discussion Papers 1165, Cowles Foundation for Research in Economics, Yale University.
    3. Lux, Thomas, 2003. "Detecting multi-fractal properties in asset returns: The failure of the scaling estimator," Economics Working Papers 2003-14, Christian-Albrechts-University of Kiel, Department of Economics.
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    Keywords

    Multifractality; Financial markets;

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