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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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    References listed on IDEAS

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    Cited by:

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