Martingales, nonstationary increments, and the efficient market hypothesis

Joseph L. McCauley, Kevin E. Bassler and Gemunu H. Gunaratne

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 15, 3916-3920

Abstract: We discuss the deep connection between nonstationary increments, martingales, and the efficient market hypothesis for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). We explain why a test for a martingale is generally a test for uncorrelated increments. We explain why martingales look Markovian at the level of both simple averages and 2-point correlations. But while a Markovian market has no memory to exploit and cannot be beaten systematically, a martingale admits memory that might be exploitable in higher order correlations. We also use the analysis of this paper to correct a misstatement of the ‘fair game’ condition in terms of serial correlations in Fama’s paper on the EMH. We emphasize that the use of the log increment as a variable in data analysis generates spurious fat tails and spurious Hurst exponents.

Keywords: Martingales; Markov processes; Memory; Stationary and nonstationary increments; Autocorrelations; Efficient market hypothesis; Fractional Brownian motion (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:15:p:3916-3920

DOI: 10.1016/j.physa.2008.01.049

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