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Multifractal geometry in stock market time series

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  • Turiel, Antonio
  • Pérez-Vicente, Conrad J.

Abstract

It has been recently noticed that time series of returns in stock markets are of multifractal (multiscaling) character. In that context, multifractality has been always evidenced by its statistical signature (i.e., the scaling exponents associated to a related variable). However, a direct geometrical framework, much more revealing about the underlying dynamics, is possible. In this paper, we present the techniques allowing the multifractal decomposition. We will show that there exists a particular fractal component, the most singular manifold (MSM), which contains the relevant information about the dynamics of the series: it is possible to reconstruct the series (at a given precision) from the MSM. We analyze the dynamics of the MSM, which shows revealing features about the evolution of this type of series.

Suggested Citation

  • Turiel, Antonio & Pérez-Vicente, Conrad J., 2003. "Multifractal geometry in stock market time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 322(C), pages 629-649.
    • Handle: RePEc:eee:phsmap:v:322:y:2003:i:c:p:629-649
    DOI: 10.1016/S0378-4371(02)01830-7
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    1. Galluccio, S. & Caldarelli, G. & Marsili, M. & Zhang, Y.-C., 1997. "Scaling in currency exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 423-436.
    2. Benoit Mandelbrot & Howard M. Taylor, 1967. "On the Distribution of Stock Price Differences," Operations Research, INFORMS, vol. 15(6), pages 1057-1062, December.
    3. A. Arnéodo & J.-F. Muzy & D. Sornette, 1998. "”Direct” causal cascade in the stock market," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 2(2), pages 277-282, March.
    4. Yanhui Liu & Parameswaran Gopikrishnan & Pierre Cizeau & Martin Meyer & Chung-Kang Peng & H. Eugene Stanley, 1999. "The statistical properties of the volatility of price fluctuations," Papers cond-mat/9903369, arXiv.org, revised Mar 1999.
    5. Yoshi Fujiwara & Hirokazu Fujisaka, 2001. "Coarse-graining and Self-similarity of Price Fluctuations," Papers cond-mat/0101175, arXiv.org.
    6. Fujiwara, Yoshi & Fujisaka, Hirokazu, 2001. "Coarse-graining and self-similarity of price fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 294(3), pages 439-446.
    7. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    8. Gopikrishnan, P & Plerou, V & Liu, Y & Amaral, L.A.N & Gabaix, X & Stanley, H.E, 2000. "Scaling and correlation in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 362-373.
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    11. Akash P. POOJARI & Siva Kiran GUPTHA & G Raghavender RAJU, 2022. "Multifractal analysis of equities. Evidence from the emerging and frontier banking sectors," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania / Editura Economica, vol. 0(3(632), A), pages 61-80, Autumn.
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