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A statistical test of market efficiency based on information theory

Author

Listed:
  • Xavier Brouty

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

  • Matthieu Garcin

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

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," Working Papers hal-03760478, HAL.
    • Handle: RePEc:hal:wpaper:hal-03760478
    Note: View the original document on HAL open archive server: https://hal.science/hal-03760478v1
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    References listed on IDEAS

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    1. Lahmiri, Salim & Bekiros, Stelios & Avdoulas, Christos, 2018. "Time-dependent complexity measurement of causality in international equity markets: A spatial approach," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 215-219.
    2. repec:cii:cepiie:2014-q4-140-60 is not listed on IDEAS
    3. Walid Mensi & Makram Beljid & Shunsuke Managi, 2014. "Structural breaks and the time-varying levels of weak-form efficiency in crude oil markets: Evidence from the Hurst exponent and Shannon entropy methods," International Economics, CEPII research center, issue 140, pages 89-106.
    4. repec:cii:cepiei:2014-q4-140-6 is not listed on IDEAS
    5. 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).
    6. Stosic, Darko & Stosic, Dusan & Ludermir, Teresa & de Oliveira, Wilson & Stosic, Tatijana, 2016. "Foreign exchange rate entropy evolution during financial crises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 233-239.
    7. 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.
    8. 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.
    9. 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.
    10. Christian Bongiorno & Damien Challet, 2022. "Statistical inference of lead-lag at various timescales between asynchronous time series from p-values of transfer entropy," Papers 2206.10173, arXiv.org.
    11. 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.
    12. 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).
    13. 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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