IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-03760478.html
   My bibliography  Save this paper

A statistical test of market efficiency based on information theory

Author

Listed:
  • Xavier Brouty

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

  • Matthieu Garcin

    (Research Center - Léonard de Vinci Pôle Universitaire - De Vinci Research Center)

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-03760478
    as

    Download full text from publisher

    File URL: https://hal.science/hal-03760478/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. repec:cii:cepiie:2014-q4-140-60 is not listed on IDEAS
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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).
    7. 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.
    8. repec:cii:cepiei:2014-q4-140-6 is not listed on IDEAS
    9. 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).
    10. 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.
    11. 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.
    12. Matthieu Garcin, 2022. "Forecasting with fractional Brownian motion: a financial perspective," Quantitative Finance, Taylor & Francis Journals, vol. 22(8), pages 1495-1512, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xavier Brouty & Matthieu Garcin, 2022. "A statistical test of market efficiency based on information theory," Papers 2208.11976, arXiv.org.
    2. Brouty, Xavier & Garcin, Matthieu, 2024. "Fractal properties, information theory, and market efficiency," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    3. Matthieu Garcin, 2023. "Complexity measure, kernel density estimation, bandwidth selection, and the efficient market hypothesis," Papers 2305.13123, arXiv.org.
    4. 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).
    5. Ayoub Ammy-Driss & Matthieu Garcin, 2021. "Efficiency of the financial markets during the COVID-19 crisis: time-varying parameters of fractional stable dynamics," Working Papers hal-02903655, HAL.
    6. Ayoub Ammy-Driss & Matthieu Garcin, 2020. "Efficiency of the financial markets during the COVID-19 crisis: time-varying parameters of fractional stable dynamics," Papers 2007.10727, arXiv.org, revised Nov 2021.
    7. Daniele Angelini & Matthieu Garcin, 2024. "Market information of the fractional stochastic regularity model," Papers 2409.07159, arXiv.org.
    8. Mensi, Walid & Tiwari, Aviral Kumar & Yoon, Seong-Min, 2017. "Global financial crisis and weak-form efficiency of Islamic sectoral stock markets: An MF-DFA analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 135-146.
    9. Matthieu Garcin, 2023. "Complexity measure, kernel density estimation, bandwidth selection, and the efficient market hypothesis," Working Papers hal-04102815, HAL.
    10. Ortiz-Cruz, Alejandro & Rodriguez, Eduardo & Ibarra-Valdez, Carlos & Alvarez-Ramirez, Jose, 2012. "Efficiency of crude oil markets: Evidences from informational entropy analysis," Energy Policy, Elsevier, vol. 41(C), pages 365-373.
    11. Andrey Shternshis & Piero Mazzarisi & Stefano Marmi, 2022. "Efficiency of the Moscow Stock Exchange before 2022," Papers 2207.10476, arXiv.org, revised Jul 2022.
    12. Matthieu Garcin, 2021. "Forecasting with fractional Brownian motion: a financial perspective," Papers 2105.09140, arXiv.org, revised Sep 2021.
    13. Aurelio F. Bariviera & Luciano Zunino & Osvaldo A. Rosso, 2016. "Crude Oil Market And Geopolitical Events: An Analysis Based On Information-Theory-Based Quantifiers," Fuzzy Economic Review, International Association for Fuzzy-set Management and Economy (SIGEF), vol. 21(1), pages 41-51, May.
    14. Vasile Brătian & Ana-Maria Acu & Camelia Oprean-Stan & Emil Dinga & Gabriela-Mariana Ionescu, 2021. "Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion," Mathematics, MDPI, vol. 9(22), pages 1-20, November.
    15. Jebabli, Ikram & Roubaud, David, 2018. "Time-varying efficiency in food and energy markets: Evidence and implications," Economic Modelling, Elsevier, vol. 70(C), pages 97-114.
    16. Busu, Cristian & Busu, Mihail, 2019. "Modeling the predictive power of the singular value decomposition-based entropy. Empirical evidence from the Dow Jones Global Titans 50 Index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    17. Andrey Shternshis & Piero Mazzarisi, 2024. "Variance of entropy for testing time-varying regimes with an application to meme stocks," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 215-258, June.
    18. Oluwasegun B. Adekoya, 2021. "Persistence and efficiency of OECD stock markets: linear and nonlinear fractional integration approaches," Empirical Economics, Springer, vol. 61(3), pages 1415-1433, September.
    19. Gu, Rongbao & Xiong, Wei & Li, Xinjie, 2015. "Does the singular value decomposition entropy have predictive power for stock market? — Evidence from the Shenzhen stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 439(C), pages 103-113.
    20. Zunino, Luciano & Zanin, Massimiliano & Tabak, Benjamin M. & Pérez, Darío G. & Rosso, Osvaldo A., 2009. "Forbidden patterns, permutation entropy and stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2854-2864.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-03760478. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.