Abstract
We reexamine the results of Serletis and Rosenberg [Serletis A, Rosenberg A. Mean rever- sion in the US stock market.
Chaos, Solitons and Fractals 2009;40:2007-2015.] who claim that the returns of the most important US stock indices (DJI, NASDAQ, NYSE and S&P500) are strongly anti-persistent and thus mean reverting. We apply various methods to detect long-range dependence - detrending moving average, detrended fluctuation analysis, gen- eralized Hurst exponent approach, classical rescaled range analysis and modified rescaled range analysis.
We show that there are no signs of anti-persistence in any of the indices. Moreover, we discuss that the authors did not find any anti-persistence but rather showed returns of the said assets do not follow the scaling power law around their moving average with varying window length.
Anti-persistence is thus spurious and due to wrong applica- tion of detrending moving average method.