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A comment on measuring the Hurst exponent of financial time series

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  • Couillard, Michel
  • Davison, Matt
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    Abstract

    A fundamental hypothesis of quantitative finance is that stock price variations are independent and can be modeled using Brownian motion. In recent years, it was proposed to use rescaled range analysis and its characteristic value, the Hurst exponent, to test for independence in financial time series. Theoretically, independent time series should be characterized by a Hurst exponent of 1/2. However, finite Brownian motion data sets will always give a value of the Hurst exponent larger than 1/2 and without an appropriate statistical test such a value can mistakenly be interpreted as evidence of long term memory. We obtain a more precise statistical significance test for the Hurst exponent and apply it to real financial data sets. Our empirical analysis shows no long-term memory in some financial returns, suggesting that Brownian motion cannot be rejected as a model for price dynamics.

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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 348 (2005)
    Issue (Month): C ()
    Pages: 404-418

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    Handle: RePEc:eee:phsmap:v:348:y:2005:i:c:p:404-418

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Econophysics; Hurst exponent; R/S analysis; Efficient market hypothesis;

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    Cited by:
    1. Ladislav Kristoufek, 2012. "How are rescaled range analyses affected by different memory and distributional properties? A Monte Carlo study," Papers 1201.3511, arXiv.org.
    2. Bassler, Kevin E. & McCauley, Joseph L. & Gunaratne, Gemunu H., 2006. "Nonstationary increments, scaling distributions, and variable diffusion processes in financial markets," MPRA Paper 2126, University Library of Munich, Germany.
    3. Abounoori, Esmaiel & Shahrazi, Mahdi & Rasekhi, Saeed, 2012. "An investigation of Forex market efficiency based on detrended fluctuation analysis: A case study for Iran," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3170-3179.
    4. Ladislav Kristoufek, 2013. "Testing power-law cross-correlations: Rescaled covariance test," Papers 1307.4727, arXiv.org, revised Aug 2013.
    5. Zhi-Qiang Jiang & Wen-Jie Xie & Wei-Xing Zhou, 2012. "Testing the weak-form efficiency of the WTI crude oil futures market," Papers 1211.4686, arXiv.org.
    6. Jozef Barunik & Ladislav Kristoufek, 2012. "On Hurst exponent estimation under heavy-tailed distributions," Papers 1201.4786, arXiv.org.
    7. Kristoufek, Ladislav, 2009. "R/S analysis and DFA: finite sample properties and confidence intervals," MPRA Paper 16446, University Library of Munich, Germany.
    8. Wegener, Christian & von Nitzsch, Rüdiger & Cengiz, Cetin, 2010. "An advanced perspective on the predictability in hedge fund returns," Journal of Banking & Finance, Elsevier, vol. 34(11), pages 2694-2708, November.
    9. Ladislav Krištoufek, 2010. "Long-Term Memory and Its Evolution in Returns of Stock Index PX Between 1997 and 2009," Politická ekonomie, University of Economics, Prague, vol. 2010(4), pages 471-487.
    10. Sergio Da Silva & Annibal Figueiredo & Iram Gleria & Raul Matsushita, 2007. "Hurst exponents, power laws, and efficiency in the Brazilian foreign exchange market," Economics Bulletin, AccessEcon, vol. 7(1), pages 1-11.
    11. repec:ebl:ecbull:v:7:y:2007:i:1:p:1-11 is not listed on IDEAS
    12. Mishra, Ritesh Kumar & Sehgal, Sanjay & Bhanumurthy, N.R., 2011. "A search for long-range dependence and chaotic structure in Indian stock market," Review of Financial Economics, Elsevier, vol. 20(2), pages 96-104, May.
    13. Kristoufek, Ladislav, 2009. "Procesy s dlouhou pamětí a jejich vývoj ve výnosech indexu PX v letech 1999 – 2009
      [Long-term memory and its evolution in returns of PX between 1999 and 2009]
      ," MPRA Paper 16435, University Library of Munich, Germany.
    14. He, Ling-Yun & Qian, Wen-Bin, 2012. "A Monte Carlo simulation to the performance of the R/S and V/S methods—Statistical revisit and real world application," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(14), pages 3770-3782.
    15. Kristoufek, Ladislav, 2009. "Distinguishing between short and long range dependence: Finite sample properties of rescaled range and modified rescaled range," MPRA Paper 16424, University Library of Munich, Germany.
    16. Matsushita, Raul & Gleria, Iram & Figueiredo, Annibal & Da Silva, Sergio, 2007. "Are Pound and Euro the Same Currency? - Updated," MPRA Paper 1981, University Library of Munich, Germany.
    17. Sánchez Granero, M.A. & Trinidad Segovia, J.E. & García Pérez, J., 2008. "Some comments on Hurst exponent and the long memory processes on capital markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5543-5551.

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