Martingales, Detrending Data, and the Efficient Market Hypothesis

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

MPRA Paper from University Library of Munich, Germany

Abstract: We discuss martingales, detrending data, and the efficient market hypothesis for stochastic processes x(t) with arbitrary diffusion coefficients D(x,t). Beginning with x-independent drift coefficients R(t) we show that Martingale stochastic processes generate uncorrelated, generally nonstationary increments. Generally, a test for a martingale is therefore a test for uncorrelated increments. A detrended process with an x- dependent drift coefficient is generally not a martingale, and so we extend our analysis to include the class of (x,t)-dependent drift coefficients of interest in finance. We explain why martingales look Markovian at the level of both simple averages and 2-point correlations. And while a Markovian market has no memory to exploit and presumably cannot be beaten systematically, it has never been shown that martingale memory cannot be exploited in 3-point or higher correlations to beat the market. We generalize our Markov scaling solutions presented earlier, and also generalize the martingale formulation of the efficient market hypothesis (EMH) to include (x,t)- dependent drift in log returns. 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 end with a discussion of Levy’scharacterization of Brownian motion and prove that an arbitrary martingale is topologically inequivalent to a Wiener process.

Keywords: Martingales; Markov processes; detrending; memory; stationary and nonstationary increments; correlations; efficient market hypothesis (search for similar items in EconPapers)
JEL-codes: C2 C53 G0 (search for similar items in EconPapers)
Date: 2007-02
New Economics Papers: this item is included in nep-ets
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Citations: View citations in EconPapers (1)

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