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Long-term Memory in Stock Market Prices


  • Andrew W. Lo


A test for long-run memory that is robust to short-range dependence is developed. It is a simple extension of Mandelbrot's "range over standard deviation" or R/S statistic, for which the relevant asymptotic sampling theory is derived via functional central limit theory. This test is applied to daily, weekly, monthly, and annual stock returns indexes over several different time periods. Contrary to previous findings, there is no evidence of long-range dependence in any of the indexes over any sample period or sub-period once short-term autocorrelations are taken into account. Illustrative Monte Carlo experiments indicate that the modified R/S test has power against at least two specific models of long-run memory, suggesting that stochastic models of short-range dependence may adequately capture the time series behavior of stock returns.

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  • Andrew W. Lo, 1989. "Long-term Memory in Stock Market Prices," NBER Working Papers 2984, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:2984
    Note: ME

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    1. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    2. Joseph G. Haubrich & Andrew W. Lo, "undated". "The Sources and Nature of Long-Term Memory in the Business Cycle," Rodney L. White Center for Financial Research Working Papers 05-89, Wharton School Rodney L. White Center for Financial Research.
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    11. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
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    13. Merton, Robert C., 1985. "On the current state of the stock market rationality hypothesis," Working papers 1717-85., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    14. Sowell, Fallaw, 1990. "The Fractional Unit Root Distribution," Econometrica, Econometric Society, vol. 58(2), pages 495-505, March.
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