IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v40y2009i4p2007-2015.html
   My bibliography  Save this article

Mean reversion in the US stock market

Author

Listed:
  • Serletis, Apostolos
  • Rosenberg, Aryeh Adam

Abstract

This paper revisits the evidence for the weaker form of the efficient market hypothesis, building on recent work by Serletis and Shintani [Serletis A, Shintani M. No evidence of chaos but some evidence of dependence in the US stock market. Chaos, Solitons & Fractals 2003;17:449–54], Elder and Serletis [Elder J, Serletis A. On fractional integrating dynamics in the US stock market. Chaos, Solitons & Fractals 2007;34;777–81], Koustas et al. [Koustas Z, Lamarche J.-F, Serletis A. Threshold random walks in the US stock market. Chaos, Solitons & Fractals, forthcoming], Hinich and Serletis [Hinich M, Serletis A. Randomly modulated periodicity in the US stock market. Chaos, Solitons & Fractals, forthcoming], and Serletis et al. [Serletis A, Uritskaya OY, Uritsky VM. Detrended Fluctuation analysis of the US stock market. Int J Bifurc Chaos, forthcoming]. In doing so, we use daily data, over the period from 5 February 1971 to 1 December 2006 (a total of 9045 observations) on four US stock market indexes – the Dow Jones Industrial Average, the Standard and Poor’s 500 Index, the NASDAQ Composite Index, and the NYSE Composite Index – and a new statistical physics approach – namely the ‘detrending moving average (DMA)’ technique, recently introduced by Alessio et al. [Alessio E, Carbone A, Castelli G, Frappietro V. Second-order moving average and scaling of stochastic time series. Euro Phys J B 2002;27;197–200.] and further developed by Carbone et al. [Carbone A, Castelli G, Stanley HE. Time dependent hurst exponent in financial time series. Physica A 2004;344;267–71, Carbone A, Castelli G, Stanley HE. Analysis of clusters formed by the moving average of a long-range correlated time series. Phys Rev E 2004;69;026105.]. The robustness of the results to the use of alternative testing methodologies is also investigated, by using Lo’s [Lo AW. Long-term memory in stock market prices. Econometrica 1991;59:1279–313.] modified rescaled range analysis. We conclude that US stock market returns display anti-persistence (mean reversion).

Suggested Citation

  • Serletis, Apostolos & Rosenberg, Aryeh Adam, 2009. "Mean reversion in the US stock market," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2007-2015.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:4:p:2007-2015
    DOI: 10.1016/j.chaos.2007.09.085
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907008296
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.09.085?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Serletis, Apostolos & Rosenberg, Aryeh Adam, 2007. "The Hurst exponent in energy futures prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 325-332.
    2. Mandelbrot, Benoit B, 1971. "When Can Price Be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models," The Review of Economics and Statistics, MIT Press, vol. 53(3), pages 225-236, August.
    3. Elder, John & Serletis, Apostolos, 2007. "On fractional integrating dynamics in the US stock market," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 777-781.
    4. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    5. 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.
    6. Arianos, Sergio & Carbone, Anna, 2007. "Detrending moving average algorithm: A closed-form approximation of the scaling law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 9-15.
    7. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    8. repec:clg:wpaper:2007-02 is not listed on IDEAS
    9. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    10. Benoit B. Mandelbrot, 1972. "Statistical Methodology for Nonperiodic Cycles: From the Covariance To R/S Analysis," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 1, number 3, pages 259-290, National Bureau of Economic Research, Inc.
    11. Fama, Eugene F, 1991. "Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-1617, December.
    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. Al-Shboul, Mohammad & Alsharari, Nizar, 2019. "The dynamic behavior of evolving efficiency: Evidence from the UAE stock markets," The Quarterly Review of Economics and Finance, Elsevier, vol. 73(C), pages 119-135.
    2. He, Shanshan & Wang, Yudong, 2017. "Revisiting the multifractality in stock returns and its modeling implications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 11-20.
    3. Mynhardt, H. R. & Plastun, Alex & Makarenko, Inna, 2014. "Behavior of Financial Markets Efficiency During the Financial Market Crisis: 2007-2009," MPRA Paper 58942, University Library of Munich, Germany.
    4. Dilip Kumar & S. Maheswaran, 2015. "Long memory in Indian exchange rates: an application of power-law scaling analysis," Macroeconomics and Finance in Emerging Market Economies, Taylor & Francis Journals, vol. 8(1-2), pages 90-107, July.
    5. Kristoufek, Ladislav, 2010. "On spurious anti-persistence in the US stock indices," Chaos, Solitons & Fractals, Elsevier, vol. 43(1), pages 68-78.
    6. Alvarez-Ramirez, J. & Rodriguez, E., 2018. "AR(p)-based detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 49-57.
    7. Ruan, Yong-Ping & Zhou, Wei-Xing, 2011. "Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1646-1654.
    8. Power, Gabriel J. & Turvey, Calum G., 2010. "Long-range dependence in the volatility of commodity futures prices: Wavelet-based evidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 79-90.
    9. Guglielmo Maria Caporale & Luis A. Gil-Alana & Alex Plastun, 2017. "Long Memory and Data Frequency in Financial Markets," Discussion Papers of DIW Berlin 1647, DIW Berlin, German Institute for Economic Research.
    10. Jiang, Zhi-Qiang & Xie, Wen-Jie & Zhou, Wei-Xing, 2014. "Testing the weak-form efficiency of the WTI crude oil futures market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 235-244.
    11. George P. Papaioannou & Christos Dikaiakos & Akylas C. Stratigakos & Panos C. Papageorgiou & Konstantinos F. Krommydas, 2019. "Testing the Efficiency of Electricity Markets Using a New Composite Measure Based on Nonlinear TS Tools," Energies, MDPI, vol. 12(4), pages 1-30, February.
    12. Rim Ammar Lamouchi, 2020. "Long Memory and Stock Market Efficiency: Case of Saudi Arabia," International Journal of Economics and Financial Issues, Econjournals, vol. 10(3), pages 29-34.
    13. Orlando, Giuseppe & Bufalo, Michele, 2022. "Modelling bursts and chaos regularization in credit risk with a deterministic nonlinear model," Finance Research Letters, Elsevier, vol. 47(PA).
    14. Onali, Enrico & Goddard, John, 2011. "Are European equity markets efficient? New evidence from fractal analysis," International Review of Financial Analysis, Elsevier, vol. 20(2), pages 59-67, April.
    15. Farzan Soleymani & Eric Paquet, 2021. "Deep Graph Convolutional Reinforcement Learning for Financial Portfolio Management -- DeepPocket," Papers 2105.08664, arXiv.org.
    16. Liu, Yang & Zhuo, Xuru & Zhou, Xiaozhu, 2024. "Multifractal analysis of Chinese literary and web novels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 641(C).
    17. Xie, Wen-Jie & Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2014. "Extreme value statistics and recurrence intervals of NYMEX energy futures volatility," Economic Modelling, Elsevier, vol. 36(C), pages 8-17.
    18. Ka Po Kung, 2022. "Efficiency of the Stock Markets after the 2008 Financial Crisis: Evidence from the Four Asian Dragons," Eurasian Journal of Business and Management, Eurasian Publications, vol. 10(2), pages 101-115.
    19. G. Papaioannou & P. Papaioannou & N. Parliaris, 2014. "Modeling the stylized facts of wholesale system marginal price (SMP) and the impacts of regulatory reforms on the Greek Electricity Market," Papers 1401.5452, arXiv.org.
    20. Ibarra-Valdez, C. & Alvarez, J. & Alvarez-Ramirez, J., 2016. "Randomness confidence bands of fractal scaling exponents for financial price returns," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 119-124.
    21. Robert Ślepaczuk & Grzegorz Zakrzewski & Paweł Sakowski, 2012. "Investment strategies beating the market. What can we squeeze from the market?," Working Papers 2012-04, Faculty of Economic Sciences, University of Warsaw.
    22. Wang, Lei & Liu, Lutao, 2020. "Long-range correlation and predictability of Chinese stock prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    23. Yang, Yan-Hong & Shao, Ying-Hui & Shao, Hao-Lin & Stanley, H. Eugene, 2019. "Revisiting the weak-form efficiency of the EUR/CHF exchange rate market: Evidence from episodes of different Swiss franc regimes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 734-746.
    24. Ślepaczuk Robert & Sakowski Paweł & Zakrzewski Grzegorz, 2018. "Investment Strategies that Beat the Market. What Can We Squeeze from the Market?," Financial Internet Quarterly (formerly e-Finanse), Sciendo, vol. 14(4), pages 36-55, December.
    25. Christian L Dunis & Jason Laws & Jozef Rudy, 2011. "Profitable mean reversion after large price drops: A story of day and night in the S&P 500, 400 MidCap and 600 SmallCap Indices," Journal of Asset Management, Palgrave Macmillan, vol. 12(3), pages 185-202, 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. Dilip Kumar & S. Maheswaran, 2015. "Long memory in Indian exchange rates: an application of power-law scaling analysis," Macroeconomics and Finance in Emerging Market Economies, Taylor & Francis Journals, vol. 8(1-2), pages 90-107, July.
    2. Anju Bala & Kapil Gupta, 2020. "Examining The Long Memory In Stock Returns And Liquidity In India," Copernican Journal of Finance & Accounting, Uniwersytet Mikolaja Kopernika, vol. 9(3), pages 25-43.
    3. Goddard, John & Onali, Enrico, 2012. "Self-affinity in financial asset returns," International Review of Financial Analysis, Elsevier, vol. 24(C), pages 1-11.
    4. Brandi, Giuseppe & Di Matteo, T., 2022. "Multiscaling and rough volatility: An empirical investigation," International Review of Financial Analysis, Elsevier, vol. 84(C).
    5. Erhard Reschenhofer & Manveer K. Mangat, 2020. "Reducing the Bias of the Smoothed Log Periodogram Regression for Financial High-Frequency Data," Econometrics, MDPI, vol. 8(4), pages 1-15, October.
    6. Mitra, S.K. & Bawa, Jaslene, 2017. "Can trade opportunities and returns be generated in a trend persistent series? Evidence from global indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 124-135.
    7. Fernández-Martínez, M. & Sánchez-Granero, M.A. & Trinidad Segovia, J.E., 2013. "Measuring the self-similarity exponent in Lévy stable processes of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5330-5345.
    8. Mynhardt, H. R. & Plastun, Alex & Makarenko, Inna, 2014. "Behavior of Financial Markets Efficiency During the Financial Market Crisis: 2007-2009," MPRA Paper 58942, University Library of Munich, Germany.
    9. Giuseppe Cavaliere, 2000. "A Rescaled Range Statistics Approach to Unit Root Tests," Econometric Society World Congress 2000 Contributed Papers 0318, Econometric Society.
    10. 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.).
    11. Sandrine Lardic & Valérie Mignon & Claude Jessua, 1996. "Les tests de mémoire longue appartiennent-ils au "camp du démon" ?," Revue Économique, Programme National Persée, vol. 47(3), pages 531-540.
    12. Jiang, Zhi-Qiang & Xie, Wen-Jie & Zhou, Wei-Xing, 2014. "Testing the weak-form efficiency of the WTI crude oil futures market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 235-244.
    13. Benjamin Rainer Auer, 2018. "Are standard asset pricing factors long-range dependent?," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 42(1), pages 66-88, January.
    14. Restocchi, Valerio & McGroarty, Frank & Gerding, Enrico, 2019. "The stylized facts of prediction markets: Analysis of price changes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 159-170.
    15. Power, Gabriel J. & Turvey, Calum G., 2010. "Long-range dependence in the volatility of commodity futures prices: Wavelet-based evidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 79-90.
    16. Serinaldi, Francesco, 2010. "Use and misuse of some Hurst parameter estimators applied to stationary and non-stationary financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2770-2781.
    17. Mouck, T., 1998. "Capital markets research and real world complexity: The emerging challenge of chaos theory," Accounting, Organizations and Society, Elsevier, vol. 23(2), pages 189-203, February.
    18. 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.
    19. Erhard Reschenhofer & Manveer K. Mangat, 2021. "Fast computation and practical use of amplitudes at non-Fourier frequencies," Computational Statistics, Springer, vol. 36(3), pages 1755-1773, September.
    20. Gil-Alana, L.A., 2006. "Fractional integration in daily stock market indexes," Review of Financial Economics, Elsevier, vol. 15(1), pages 28-48.

    More about this item

    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:eee:chsofr:v:40:y:2009:i:4:p:2007-2015. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.