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Martingales, the efficient market hypothesis, and spurious stylized facts


  • McCauley, Joseph L.
  • Bassler, Kevin E.
  • Gunaratne, Gemunu h.


The condition for stationary increments, not scaling, detemines long time pair autocorrelations. An incorrect assumption of stationary increments generates spurious stylized facts, fat tails and a Hurst exponent Hs=1/2, when the increments are nonstationary, as they are in FX markets. The nonstationarity arises from systematic uneveness in noise traders’ behavior. Spurious results arise mathematically from using a log increment with a ‘sliding window’. We explain why a hard to beat market demands martingale dynamics , and martingales with nonlinear variance generate nonstationary increments. The nonstationarity is exhibited directly for Euro/Dollar FX data. We observe that the Hurst exponent Hs generated by the using the sliding window technique on a time series plays the same role as does Mandelbrot’s Joseph exponent. Finally, Mandelbrot originally assumed that the ‘badly behaved second moment of cotton returns is due to fat tails, but that nonconvergent behavior is instead direct evidence for nonstationary increments. Summarizing, the evidence for scaling and fat tails as the basis for econophysics and financial economics is provided neither by FX markets nor by cotton price data.

Suggested Citation

  • McCauley, Joseph L. & Bassler, Kevin E. & Gunaratne, Gemunu h., 2007. "Martingales, the efficient market hypothesis, and spurious stylized facts," MPRA Paper 5303, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:5303

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    References listed on IDEAS

    1. McCauley, Joseph L., 2007. "Fokker-Planck and Chapman-Kolmogorov equations for Ito processes with finite memory," MPRA Paper 2128, University Library of Munich, Germany.
    2. Joseph L. McCauley, 2007. "Fokker-Planck and Chapman-Kolmogorov equations for Ito processes with finite memory," Papers cond-mat/0702517,, revised Feb 2007.
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    Cited by:

    1. McCauley, Joseph L., 2007. "A comment on the paper “Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker–Planck equations” by T.D. Frank," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(2), pages 445-452.

    More about this item


    Nonstationary increments; martingales; fat tails; Hurst exponent scaling;

    JEL classification:

    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

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