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Mean reversion in the US stock market

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  • 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).

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  • 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
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    References listed on IDEAS

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    1. Fama, Eugene F, 1991. "Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-1617, December.
    2. 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.
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    6. 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.
    7. 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.
    8. Farzan Soleymani & Eric Paquet, 2021. "Deep Graph Convolutional Reinforcement Learning for Financial Portfolio Management -- DeepPocket," Papers 2105.08664, arXiv.org.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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).
    22. 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.
    23. 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).
    24. 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.

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