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Empirically Based Modeling in the Social Sciences and Spurious Stylized Facts

Bassler, Kevin E. and Gunaratne, Gemunu H. and McCauley, Joseph L. (2007): Empirically Based Modeling in the Social Sciences and Spurious Stylized Facts.

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The discovery of the dynamics of a time series requires construction of the transition density, 1-point densities and scaling exponents provide no knowledge of the dynamics. Time series require some sort of statistical regularity, otherwise there is no basis for analysis. We state the possible tests for statistical regularity in terms of increments. 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’. The Hurst exponent Hs generated by the using the sliding window technique on a time series plays the same role as Mandelbrot’s Joseph exponent. Mandelbrot originally assumed that the ‘badly behaved second moment of cotton returns is due to fat tails, but that nonconvergent behavior providess instead direct evidence for nonstationary increments.

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