Bassler, Kevin E. and Gunaratne, Gemunu H. and McCauley, Joseph L. (2007): Empirically Based Modeling in the Social Sciences and Spurious Stylized Facts.
Download (1MB) | Preview
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.
|Item Type:||MPRA Paper|
|Original Title:||Empirically Based Modeling in the Social Sciences and Spurious Stylized Facts|
|Keywords:||Stylized facts, nonstationary time series analysis,regression, martingales, uncorrelated increments, fat tails, efficient market hypothesis,sliding windows|
|Subjects:||C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation
C - Mathematical and Quantitative Methods > C2 - Single Equation Models; Single Variables > C22 - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
|Depositing User:||Joseph L. McCauley|
|Date Deposited:||18. Nov 2007 18:21|
|Last Modified:||14. Feb 2013 03:48|
1. J.L. McCauley, K.E. Bassler, and G.H. Gunaratne, Martingales, Detranding Data, and the Efficient Market Hypothesis, a A37, 202, 2008. 2. K.E. Bassler, J. L. McCauley, & G.H. Gunaratne, Nonstationary Increments, Scaling Distributions, and Variable Diffusion Processes in Financial Markets, PNAS 104, 17297, 23 Oct. 2008. 3. J. L. McCauley, K.E. Bassler, & G.H. Gunaratne, On the Analysis of Time Series with Nonstationary Increments in Handbook of Complexity Research, ed. B. Rosser, 2008. 4. P. Embrechts and M. Maejima, Selfsimilar Processes, Princeton University Press, Princeton, 2002. 5.B. Mandelbrot & J. W. van Ness, SIAM Rev. 10, 2, 422,1968. 6. B. Mandelbrot and M.S. Taqqu, 42nd Session of the International Statistical Institute of Manila, 1, 4-14 Dec. 1979. 7. J. L. McCauley, G. H. Gunaratne, and K. E. Bassler, Hurst Exponents, Markov Processes, and Fractional Brownian Motion, Physica A 369: 343 (2006). 8. K.E. Bassler, G.H. Gunaratne, & J. L. McCauley, Hurst Exponents, Markov Processes, and Nonlinear Diffusion Equations, Physica A (2006). 9. P. Hänggi, H. Thomas, H. Grabert, and P. Talkner, J. Stat. Phys. 18, 155, 1978. 10. J.L. McCauley, Dynamics of Markets: Econophysics and Finance, Cambridge, Cambridge, 2004. 121. E. Fama, J. Finance 25, 383-417, 1970. 12.See http://www.xycoon.com/non_stationary_time_series.htm and related papers on regression analysis. 13. T. Di Matteo, T.Aste, & M.M. Dacorogna, Physica A324, 183, 2003. 14. R.L. Stratonovich. Topics in the Theory of Random Noise, Gordon & Breach: N.Y., tr. R. A. Silverman, 1963. 15. B. Mandelbrot, J. Business 36, 420, 1963. 16. J.L. McCauley, Markov vs. nonMarkovian processes: A comment on the paper ‘Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker-Planck equations’ by T.D. Frank, Physica A382, 445, 2007. 17. J.L. McCauley, Ito Processes with Finitely Many States of Memory, preprint, 2007. 18. G.H. Gunaratne & J.L. McCauley. Proc. of SPIE conf. on Noise & Fluctuations 2005, 5848,131, 2005. 19. A. L. Alejandro-Quinones, K.E. Bassler, M. Field, J.L. McCauley, M. Nicol, I. Timofeyev, A. Török, and G.H. Gunaratne, Physica 363A, 383, 2006. 20. M.C. Wang & G.E. Uhlenbeck in Selected Papers on Noise and Stochastic Processes, ed. N. Wax, Dover: N.Y., 1954. 21. J. L. McCauley, G.H. Gunaratne, & K.E. Bassler, Martingale Option Pricing, Physica A380, 351, 2007. 22. A.M. Yaglom & I.M. Yaglom, An introduction to the Theory of Stationary Random Functions. Transl. and ed. by R. A. Silverman. Prentice-Hall: Englewood Cliffs, N.J., 1962. 23. E.P. Wigner, Symmetries and Reflections. Univ. Indiana: Bloomington,1967. 24. J.L. McCauley, Classical Mechanics: flows, transformations, integrability and chaos. Cambridge Univ. Pr., Cambridge, 1997. 25. C.H. Hommes, PNAS 99, Suppl. 3, 7221, 2002. 26. S. Gallucio, G. Caldarelli, M. Marsilli, and Y.-C. Zhang, Physica A245, 423, 1997. 27. L. Borland, Phys. Rev. E57, 6634, 1998. 28. J.A. Skjeltorp, Fractal Scaling Behaviour in the Norwegian Stock Market, Masters thesis, Norwegian School of Management, 1996. 29. B. Mandelbrot in P. Cootner, The Random Character of Stock Market Prices, MIT Pr., Cambridge, Mass., 1964.