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Fractal properties, information theory, and market efficiency

Author

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  • Xavier Brouty

    (ESILV - École Supérieure d'Ingénierie Léonard de Vinci)

  • Matthieu Garcin

    (DVRC - De Vinci Research Center - DVHE - De Vinci Higher Education)

Abstract

Considering that both the entropy-based market information and the Hurst exponent are useful tools for determining whether the efficient market hypothesis holds for a given asset, we study the link between the two approaches. We thus provide a theoretical expression for the market information when log-prices follow either a fractional Brownian motion or its stationary extension using the Lamperti transform. In the latter model, we show that a Hurst exponent close to 1/2 can lead to a very high informativeness of the time series, because of the stationarity mechanism. In addition, we introduce a multiscale method to get a deeper interpretation of the entropy and of the market information, depending on the size of the information set. Applications to Bitcoin, CAC 40 index, Nikkei 225 index, and EUR/USD FX rate, using daily or intraday data, illustrate the methodological content.

Suggested Citation

  • Xavier Brouty & Matthieu Garcin, 2023. "Fractal properties, information theory, and market efficiency," Working Papers hal-04138656, HAL.
    • Handle: RePEc:hal:wpaper:hal-04138656
    Note: View the original document on HAL open archive server: https://hal.science/hal-04138656v1
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    References listed on IDEAS

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    1. Bacry, E. & Delour, J. & Muzy, J.F., 2001. "Modelling financial time series using multifractal random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 84-92.
    2. Alvarez-Ramirez, Jose & Rodriguez, Eduardo, 2021. "A singular value decomposition entropy approach for testing stock market efficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    3. Ammy-Driss, Ayoub & Garcin, Matthieu, 2023. "Efficiency of the financial markets during the COVID-19 crisis: Time-varying parameters of fractional stable dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
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    Cited by:

    1. Matthieu Garcin, 2023. "Complexity measure, kernel density estimation, bandwidth selection, and the efficient market hypothesis," Working Papers hal-04102815, HAL.

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