dorsal/arxiv
View SchemaMartingales, Detrending Data, and the Efficient Market Hypothesis
| Authors | Joseph L. McCauley, Kevin E. Bassler, Gemunu H. Gunaratne |
|---|---|
| Categories | |
| ArXiv ID | physics/0701264 |
| URL | https://arxiv.org/abs/physics/0701264 |
| DOI | 10.1016/j.physa.2007.08.019 |
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.
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"abstract": "We discuss martingales, detrending data, and the efficient market hypothesis\nfor stochastic processes x(t) with arbitrary diffusion coefficients D(x,t).\nBeginning with x-independent drift coefficients R(t) we show that Martingale\nstochastic processes generate uncorrelated, generally nonstationary increments.\nGenerally, a test for a martingale is therefore a test for uncorrelated\nincrements. A detrended process with an x- dependent drift coefficient is\ngenerally not a martingale, and so we extend our analysis to include the class\nof (x,t)-dependent drift coefficients of interest in finance. We explain why\nmartingales look Markovian at the level of both simple averages and 2-point\ncorrelations. And while a Markovian market has no memory to exploit and\npresumably cannot be beaten systematically, it has never been shown that\nmartingale memory cannot be exploited in 3-point or higher correlations to beat\nthe market. We generalize our Markov scaling solutions presented earlier, and\nalso generalize the martingale formulation of the efficient market hypothesis\n(EMH) to include (x,t)-dependent drift in log returns. We also use the analysis\nof this paper to correct a misstatement of the fair game condition in terms of\nserial correlations in Fama\u0027s paper on the EMH.",
"arxiv_id": "physics/0701264",
"authors": [
"Joseph L. McCauley",
"Kevin E. Bassler",
"Gemunu H. Gunaratne"
],
"categories": [
"physics.soc-ph",
"physics.data-an",
"q-fin.ST"
],
"doi": "10.1016/j.physa.2007.08.019",
"title": "Martingales, Detrending Data, and the Efficient Market Hypothesis",
"url": "https://arxiv.org/abs/physics/0701264"
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