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Dynamical Hurst exponent as a tool to monitor unstable periods in financial time series

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  • Raffaello Morales
  • T. Di Matteo
  • Ruggero Gramatica
  • Tomaso Aste
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    Abstract

    We investigate the use of the Hurst exponent, dynamically computed over a moving time-window, to evaluate the level of stability/instability of financial firms. Financial firms bailed-out as a consequence of the 2007-2010 credit crisis show a neat increase with time of the generalized Hurst exponent in the period preceding the unfolding of the crisis. Conversely, firms belonging to other market sectors, which suffered the least throughout the crisis, show opposite behaviors. These findings suggest the possibility of using the scaling behavior as a tool to track the level of stability of a firm. In this paper, we introduce a method to compute the generalized Hurst exponent which assigns larger weights to more recent events with respect to older ones. In this way large fluctuations in the remote past are less likely to influence the recent past. We also investigate the scaling associated with the tails of the log-returns distributions and compare this scaling with the scaling associated with the Hurst exponent, observing that the processes underlying the price dynamics of these firms are truly multi-scaling.

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    File URL: http://arxiv.org/pdf/1109.0465
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1109.0465.

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    Date of creation: Sep 2011
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    Publication status: Published in Physica A 391, 2012, 3180-3189
    Handle: RePEc:arx:papers:1109.0465

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    Web page: http://arxiv.org/

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    1. Patrick A. Groenendijk & André Lucas & Casper G. de Vries, 1998. "A Hybrid Joint Moment Ratio Test for Financial Time Series," Tinbergen Institute Discussion Papers 98-104/2, Tinbergen Institute.
    2. Ruipeng Liu & Tiziana Di Matteo & Thomas Lux, 2008. "Multifractality and Long-Range Dependence of Asset Returns: The Scaling Behaviour of the Markov-Switching Multifractal Model with Lognormal Volatility Components," Kiel Working Papers 1427, Kiel Institute for the World Economy.
    3. Jean-Philippe Bouchaud & Marc Potters & Martin Meyer, 1999. "Apparent multifractality in financial time series," Science & Finance (CFM) working paper archive 9906347, Science & Finance, Capital Fund Management.
    4. Laurent Calvet & Adlai Fisher, 2002. "Multifractality In Asset Returns: Theory And Evidence," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 381-406, August.
    5. Liu, Ruipeng & Di Matteo, Tiziana & Lux, Thomas, 2007. "True and Apparent Scaling: The Proximity of the Markov- Switching Multifractal Model to Long-Range Dependence," Economics Working Papers 2007,06, Christian-Albrechts-University of Kiel, Department of Economics.
    6. Taisei Kaizoji, 2003. "Scaling behavior in land markets," Papers cond-mat/0302470, arXiv.org, revised Mar 2006.
    7. T. Di Matteo & T. Aste & Michel M. Dacorogna, 2005. "Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development," Econometrics 0503004, EconWPA.
    8. Jozef Barunik & Ladislav Kristoufek, 2012. "On Hurst exponent estimation under heavy-tailed distributions," Papers 1201.4786, arXiv.org.
    9. Scalas, Enrico, 1998. "Scaling in the market of futures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 253(1), pages 394-402.
    10. Laurent Calvet & Adlai Fisher & Benoit Mandelbrot, 1999. "A Multifractal Model of Assets Returns," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-072, New York University, Leonard N. Stern School of Business-.
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