Mean reversion in the US stock market

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).