IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/16424.html
   My bibliography  Save this paper

Distinguishing between short and long range dependence: Finite sample properties of rescaled range and modified rescaled range

Author

Listed:
  • Kristoufek, Ladislav

Abstract

Mostly used estimators of Hurst exponent for detection of long-range dependence are biased by presence of short-range dependence in the underlying time series. We present confidence intervals estimates for rescaled range and modified rescaled range. We show that the difference in expected values and confidence intervals enables us to use both methods together to clearly distinguish between the two types of processes. The estimates are further applied on Dow Jones Industrial Average between 1944 and 2009 and show that returns do not show any long-range dependence whereas volatility shows both short-range and long-range dependence in the underlying process.

Suggested Citation

  • 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.
    • Handle: RePEc:pra:mprapa:16424
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/16424/2/MPRA_paper_16424.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. Chin, Wencheong, 2008. "Spurious long-range dependence: evidence from Malaysian equity markets," MPRA Paper 7914, University Library of Munich, Germany.
    3. 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.
    4. Lux, Thomas, 2007. "Applications of statistical physics in finance and economics," Economics Working Papers 2007-05, Christian-Albrechts-University of Kiel, Department of Economics.
    5. Paul Eitelman & Justin Vitanza, 2008. "A non-random walk revisited: short- and long-term memory in asset prices," International Finance Discussion Papers 956, Board of Governors of the Federal Reserve System (U.S.).
    6. 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.
    7. 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.
    8. Lennart Berg & Johan Lyhagen, 1998. "Short and long-run dependence in Swedish stock returns," Applied Financial Economics, Taylor & Francis Journals, vol. 8(4), pages 435-443.
    9. Andreas S. Andreou & George A. Zombanakis, 2006. "Computational Intelligence in Exchange-Rate Forecasting," Working Papers 49, Bank of Greece.
    10. 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.
    11. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    12. 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.
    13. 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.
    14. T. Di Matteo, 2007. "Multi-scaling in finance," Quantitative Finance, Taylor & Francis Journals, vol. 7(1), pages 21-36.
    15. 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.
    16. 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.
    17. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    18. 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.
    19. 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.
    20. Lisa Borland & Jean-Philippe Bouchaud & Jean-Francois Muzy & Gilles Zumbach, 2005. "The Dynamics of Financial Markets -- Mandelbrot's multifractal cascades, and beyond," Science & Finance (CFM) working paper archive 500061, Science & Finance, Capital Fund Management.
    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. Gomes, Luís M. P. & Soares, Vasco J. S. & Gama, Sílvio M. A. & Matos, José A. O., 2018. "Long-term memory in Euronext stock indexes returns: an econophysics approach," Business and Economic Horizons (BEH), Prague Development Center, vol. 14(4), pages 862-881, August.

    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. Kristoufek, Ladislav, 2009. "R/S analysis and DFA: finite sample properties and confidence intervals," MPRA Paper 16446, University Library of Munich, Germany.
    2. 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.
    3. 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.
    4. 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.
    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. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Kristoufek, Ladislav, 2010. "On spurious anti-persistence in the US stock indices," Chaos, Solitons & Fractals, Elsevier, vol. 43(1), pages 68-78.
    13. Auer, Benjamin R., 2016. "On time-varying predictability of emerging stock market returns," Emerging Markets Review, Elsevier, vol. 27(C), pages 1-13.
    14. Miguel Ángel Sánchez & Juan E Trinidad & José García & Manuel Fernández, 2015. "The Effect of the Underlying Distribution in Hurst Exponent Estimation," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-17, May.
    15. Guglielmo Maria Caporale & Luis A. Gil-Alana & Alex Plastun, 2017. "Long Memory and Data Frequency in Financial Markets," CESifo Working Paper Series 6396, CESifo.
    16. Ma, Pengcheng & Li, Daye & Li, Shuo, 2016. "Efficiency and cross-correlation in equity market during global financial crisis: Evidence from China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 163-176.
    17. 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.
    18. 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.
    19. 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.
    20. Avci-Surucu, Ezgi & Aydogan, A. Kursat & Akgul, Doganbey, 2016. "Bidding structure, market efficiency and persistence in a multi-time tariff setting," Energy Economics, Elsevier, vol. 54(C), pages 77-87.

    More about this item

    Keywords

    rescaled range; modified rescaled range; Hurst exponent; long-range dependence; confidence intervals;
    All these keywords.

    JEL classification:

    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - 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:16424. 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.