Martingales, the efficient market hypothesis, and spurious stylized facts

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

MPRA Paper from University Library of Munich, Germany

Abstract: 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.

Keywords: Nonstationary increments; martingales; fat tails; Hurst exponent scaling (search for similar items in EconPapers)
JEL-codes: C40 G15 (search for similar items in EconPapers)
Date: 2007-10-12
New Economics Papers: this item is included in nep-ets
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Citations: View citations in EconPapers (2)

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