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Stock market prices and long-range dependence


  • Murad S. Taqqu

    (Boston University, Department of Mathematics, Boston, MA 02215, USA Manuscript)

  • Vadim Teverovsky

    (Boston University, Department of Mathematics, Boston, MA 02215, USA Manuscript)

  • Walter Willinger

    () (AT&T Labs-Research, 180 Park Avenue, C284, Florham Park, NJ 07932, USA)


Using the CRSP (Center for Research in Security Prices) daily stock return data, we revisit the question of whether or not actual stock market prices exhibit long-range dependence. Our study is based on an empirical investigation reported in Teverovsky, Taqqu and Willinger [33] of the modified rescaled adjusted range or R/S statistic that was proposed by Lo [17] as a test for long-range dependence with good robustness properties under "extra" short-range dependence. Our main conclusion is that because the modified R/S statistic shows a strong preference for accepting the null hypothesis of no long-range dependence, irrespective of whether long-range dependence is present in the data or not, Lo's acceptance of the hypothesis for the CRSP data (i.e., no long-range dependence in stock market prices) is less conclusive than is usually regarded in the econometrics literature. In fact, upon further analysis of the data, we find empirical evidence of long-range dependence in stock price returns, but because the corresponding degree of long-range dependence (measured via the Hurst parameter H) is typically very low (i.e., H-values around 0.60), the evidence is not absolutely conclusive.

Suggested Citation

  • Murad S. Taqqu & Vadim Teverovsky & Walter Willinger, 1999. "Stock market prices and long-range dependence," Finance and Stochastics, Springer, vol. 3(1), pages 1-13.
  • Handle: RePEc:spr:finsto:v:3:y:1999:i:1:p:1-13
    Note: received: May 1997; final version received: September 1997

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    Cited by:

    1. Raul Matsushita & Andre Santos & Iram Gleria & Annibal Figueiredo & Sergio Da Silva, 2005. "Are Pound and Euro the Same Currency?," International Finance 0505002, EconWPA.

    More about this item


    Long-range dependence; fractional Gaussian noise; fractional ARIMA; long memory;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)


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