IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/16446.html
   My bibliography  Save this paper

R/S analysis and DFA: finite sample properties and confidence intervals

Author

Listed:
  • Kristoufek, Ladislav

Abstract

We focus on finite sample properties of two mostly used methods of Hurst exponent H estimation – R/S analysis and DFA. Even though both methods have been widely applied on different types of financial assets, only several papers have dealt with finite sample properties which are crucial as the properties differ significantly from the asymptotic ones. Recently, R/S analysis has been shown to overestimate H when compared with DFA. However, we show on the random time series with lengths from 2^9 to 2^17 that even though the estimates of R/S are truly significantly higher than an asymptotic limit of 0.5, they remain very close to the estimates proposed by Anis & Lloyd and the estimated standard deviations are lower than the ones of DFA. On the other hand, DFA estimates are very close to 0.5. The results propose that R/S still remains useful and robust method even when compared to newer method of DFA which is usually preferred in recent literature.

Suggested Citation

  • Kristoufek, Ladislav, 2009. "R/S analysis and DFA: finite sample properties and confidence intervals," MPRA Paper 16446, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:16446
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/16446/1/MPRA_paper_16446.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Grech, D & Mazur, Z, 2004. "Can one make any crash prediction in finance using the local Hurst exponent idea?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 133-145.
    2. Czarnecki, Łukasz & Grech, Dariusz & Pamuła, Grzegorz, 2008. "Comparison study of global and local approaches describing critical phenomena on the Polish stock exchange market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6801-6811.
    3. Weron, Rafał, 2002. "Estimating long-range dependence: finite sample properties and confidence intervals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(1), pages 285-299.
    4. Lillo Fabrizio & Farmer J. Doyne, 2004. "The Long Memory of the Efficient Market," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(3), pages 1-35, September.
    5. John T. Barkoulas & Christopher F. Baum & Nickolaos Travlos, 1996. "Long Memory in the Greek Stock Market," Boston College Working Papers in Economics 356., Boston College Department of Economics.
    6. Jarque, Carlos M. & Bera, Anil K., 1980. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals," Economics Letters, Elsevier, vol. 6(3), pages 255-259.
    7. Alvarez-Ramirez, Jose & Alvarez, Jesus & Rodriguez, Eduardo & Fernandez-Anaya, Guillermo, 2008. "Time-varying Hurst exponent for US stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6159-6169.
    8. Alvarez-Ramirez, Jose & Rodriguez, Eduardo & Carlos Echeverría, Juan, 2005. "Detrending fluctuation analysis based on moving average filtering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 199-219.
    9. Matteo, T. Di & Aste, T. & Dacorogna, Michel M., 2005. "Long-term memories of developed and emerging markets: Using the scaling analysis to characterize their stage of development," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 827-851, April.
    10. T. Di Matteo, 2007. "Multi-scaling in finance," Quantitative Finance, Taylor & Francis Journals, vol. 7(1), pages 21-36.
    11. Couillard, Michel & Davison, Matt, 2005. "A comment on measuring the Hurst exponent of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 404-418.
    12. Matos, José A.O. & Gama, Sílvio M.A. & Ruskin, Heather J. & Sharkasi, Adel Al & Crane, Martin, 2008. "Time and scale Hurst exponent analysis for financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3910-3915.
    13. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    14. Carbone, A. & Castelli, G. & Stanley, H.E., 2004. "Time-dependent Hurst exponent in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 267-271.
    15. Bera, Anil K. & Jarque, Carlos M., 1981. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals : Monte Carlo Evidence," Economics Letters, Elsevier, vol. 7(4), pages 313-318.
    Full references (including those not matched with items on IDEAS)

    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. Barunik, Jozef & Kristoufek, Ladislav, 2010. "On Hurst exponent estimation under heavy-tailed distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3844-3855.
    2. 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.
    3. Ladislav Krištoufek, 2010. "Dlouhá paměť a její vývoj ve výnosech burzovního indexu PX v letech 1997-2009 [Long-Term Memory and Its Evolution in Returns of Stock Index PX Between 1997 and 2009]," Politická ekonomie, Prague University of Economics and Business, vol. 2010(4), pages 471-487.
    4. 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.
    5. Kristoufek, Ladislav, 2012. "How are rescaled range analyses affected by different memory and distributional properties? A Monte Carlo study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(17), pages 4252-4260.
    6. Li, Daye & Nishimura, Yusaku & Men, Ming, 2016. "The long memory and the transaction cost in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 312-320.
    7. Anagnostidis, P. & Varsakelis, C. & Emmanouilides, C.J., 2016. "Has the 2008 financial crisis affected stock market efficiency? The case of Eurozone," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 116-128.
    8. Lin, Xiaoqiang & Fei, Fangyu, 2013. "Long memory revisit in Chinese stock markets: Based on GARCH-class models and multiscale analysis," Economic Modelling, Elsevier, vol. 31(C), pages 265-275.
    9. Adam Karp & Gary Van Vuuren, 2019. "Investment Implications Of The Fractal Market Hypothesis," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 1-27, March.
    10. Kristoufek, Ladislav, 2010. "On spurious anti-persistence in the US stock indices," Chaos, Solitons & Fractals, Elsevier, vol. 43(1), pages 68-78.
    11. Zunino, Luciano & Bariviera, Aurelio F. & Guercio, M. Belén & Martinez, Lisana B. & Rosso, Osvaldo A., 2016. "Monitoring the informational efficiency of European corporate bond markets with dynamical permutation min-entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 1-9.
    12. A. Gómez-Águila & J. E. Trinidad-Segovia & M. A. Sánchez-Granero, 2022. "Improvement in Hurst exponent estimation and its application to financial markets," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-21, December.
    13. Sukpitak, Jessada & Hengpunya, Varagorn, 2016. "The influence of trading volume on market efficiency: The DCCA approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 259-265.
    14. Li, Daye & Nishimura, Yusaku & Men, Ming, 2016. "Why the long-term auto-correlation has not been eliminated by arbitragers: Evidences from NYMEX," Energy Economics, Elsevier, vol. 59(C), pages 167-178.
    15. Ladislav Kristoufek & Miloslav Vosvrda, 2014. "Measuring capital market efficiency: long-term memory, fractal dimension and approximate entropy," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(7), pages 1-9, July.
    16. Bariviera, Aurelio F., 2021. "One model is not enough: Heterogeneity in cryptocurrencies’ multifractal profiles," Finance Research Letters, Elsevier, vol. 39(C).
    17. Vogl, Markus, 2023. "Hurst exponent dynamics of S&P 500 returns: Implications for market efficiency, long memory, multifractality and financial crises predictability by application of a nonlinear dynamics analysis framewo," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    18. Auer, Benjamin R., 2016. "On time-varying predictability of emerging stock market returns," Emerging Markets Review, Elsevier, vol. 27(C), pages 1-13.
    19. Sukpitak, Jessada & Hengpunya, Varagorn, 2016. "Efficiency of Thai stock markets: Detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 204-209.
    20. Ladislav Kristoufek, 2012. "Fractal Markets Hypothesis And The Global Financial Crisis: Scaling, Investment Horizons And Liquidity," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 15(06), pages 1-13.

    More about this item

    Keywords

    rescaled range analysis; detrended fluctuation analysis; Hurst exponent; long-range dependence; confidence intervals;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C59 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Other
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:pra:mprapa:16446. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.