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Shuffling for understanding multifractality, application to asset price time series

Author

Listed:
  • Patrice Abry

    (Phys-ENS - Laboratoire de Physique de l'ENS Lyon - ENS de Lyon - École normale supérieure de Lyon - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - CNRS - Centre National de la Recherche Scientifique)

  • Yannick Malevergne

    (PRISM Sorbonne - Pôle de recherche interdisciplinaire en sciences du management - UP1 - Université Paris 1 Panthéon-Sorbonne)

  • Herwig Wendt

    (IRIT-MINDS - CoMputational imagINg anD viSion - IRIT - Institut de recherche en informatique de Toulouse - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - UT2J - Université Toulouse - Jean Jaurès - UT - Université de Toulouse - UT3 - Université Toulouse III - Paul Sabatier - UT - Université de Toulouse - CNRS - Centre National de la Recherche Scientifique - Toulouse INP - Institut National Polytechnique (Toulouse) - UT - Université de Toulouse - TMBI - Toulouse Mind & Brain Institut - UT2J - Université Toulouse - Jean Jaurès - UT - Université de Toulouse - UT3 - Université Toulouse III - Paul Sabatier - UT - Université de Toulouse, CNRS - Centre National de la Recherche Scientifique)

  • Marc Senneret
  • Laurent Jaffrès
  • Blaise Liaustrat
Abstract
Multifractal analysis has become a standard signal processing tool successfully used to model scale-free temporal dynamics in many applications, very different in nature. This is notably the case in financial engineering where, after Man-delbrot's seminal contributions, multifractal models have been used since the late 90ies to describe temporal fluctuations in asset prices. However, what exact features of temporal dynamics are actually encoded in multifractal properties remains generally only partially understood. In finance, notably, multifractality is associated to the burstiness of the returns, yet its relation to trends (signs of the returns) or volatility (modulus of the returns) remains unclear. Comparing the estimated multifractal properties of well-controlled synthetic multifractal processes to those of surrogate data, obtained by applying random permutations (shuffling) either to signs, or to modulus, or to both, of increments of original data, permits to better understand what aspects of temporal dynamics are captured by multifractality. The same procedure applied to a large dataset of asset prices entering the composition of the Eurostoxx600 index permits to evidence a simple and solid relation between multifractality and volatility as well as a weaker and complicated relation to returns.

Suggested Citation

  • Patrice Abry & Yannick Malevergne & Herwig Wendt & Marc Senneret & Laurent Jaffrès & Blaise Liaustrat, 2019. "Shuffling for understanding multifractality, application to asset price time series," Post-Print hal-02361738, HAL.
    • Handle: RePEc:hal:journl:hal-02361738
    Note: View the original document on HAL open archive server: https://hal.science/hal-02361738
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    References listed on IDEAS

    as
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