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A statistical test of market efficiency based on information theory

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  • Xavier Brouty
  • Matthieu Garcin

Abstract

We determine the amount of information contained in a time series of price returns at a given time scale, by using a widespread tool of the information theory, namely the Shannon entropy, applied to a symbolic representation of this time series. By deriving the exact and the asymptotic distribution of this market information indicator in the case where the efficient market hypothesis holds, we develop a statistical test of market efficiency. We apply it to a real dataset of stock indices, single stock, and cryptocurrency, for which we are able to determine at each date whether the efficient market hypothesis is to be rejected, with respect to a given confidence level.

Suggested Citation

  • Xavier Brouty & Matthieu Garcin, 2022. "A statistical test of market efficiency based on information theory," Papers 2208.11976, arXiv.org.
    • Handle: RePEc:arx:papers:2208.11976
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    References listed on IDEAS

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    2. Risso, Wiston Adrián, 2008. "The informational efficiency and the financial crashes," Research in International Business and Finance, Elsevier, vol. 22(3), pages 396-408, September.
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    7. Espinosa-Paredes, G. & Rodriguez, E. & Alvarez-Ramirez, J., 2022. "A singular value decomposition entropy approach to assess the impact of Covid-19 on the informational efficiency of the WTI crude oil market," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    8. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    9. Garcin, Matthieu, 2017. "Estimation of time-dependent Hurst exponents with variational smoothing and application to forecasting foreign exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 462-479.
    10. Shternshis, Andrey & Mazzarisi, Piero & Marmi, Stefano, 2022. "Measuring market efficiency: The Shannon entropy of high-frequency financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    11. Matthieu Garcin, 2019. "Hurst Exponents And Delampertized Fractional Brownian Motions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(05), pages 1-26, August.
    12. Matthieu Garcin, 2022. "Forecasting with fractional Brownian motion: a financial perspective," Quantitative Finance, Taylor & Francis Journals, vol. 22(8), pages 1495-1512, August.
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    Cited by:

    1. 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).
    2. Jessica Morales Herrera & Ra'ul Salgado-Garc'ia, 2023. "Trend patterns statistics for assessing irreversibility in cryptocurrencies: time-asymmetry versus inefficiency," Papers 2307.08612, arXiv.org.

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