Bassler, Kevin E. Gunaratne, Gemunu H. McCauley, Joseph L.
Abstract
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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Publisher Info
Paper provided by University Library of Munich, Germany in its series MPRA Paper with number
5813.
Find related papers by JEL classification: C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models
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References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
McCauley, Joseph L. & Gunaratne, Gemunu H. & Bassler, Kevin E., 2007.
"Martingale option pricing,"
MPRA Paper
2151, University Library of Munich, Germany.
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