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Short-term Dependence in Time Series as an Index of Complexity: Example from the S&P-500 Index

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  • Dominique, C-Rene
  • Rivera-Solis, Luis Eduardo

Abstract

The capital market is a reflexive dynamical input/output construct whose output (time series) is usually assessed by an index of roughness known as Hurst’s exponent (H). Oddly enough, H has no theoretical foundation, but recently it has been found experimentally to vary from persistence (H > 1/2) or long-term dependence to anti-persistence (H

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 41408.

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Date of creation: 01 Mar 2012
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Publication status: Published in International Business Research No. 9.Volume(2012): pp. 38-48
Handle: RePEc:pra:mprapa:41408

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Keywords: Hurst Exponent; anti-persistence; fractal attractors; SDIC; chaos; inherent noise; market crashes; Renyi’s generalized fractal dimensions;

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References

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  1. Invernizzi, Sergio & Medio, Alfredo, 1991. "On lags and chaos in economic dynamic models," Journal of Mathematical Economics, Elsevier, vol. 20(6), pages 521-550.
  2. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 16(3), pages 261-68, July.
  3. Thomas Lux, 1996. "Long-term stochastic dependence in financial prices: evidence from the German stock market," Applied Economics Letters, Taylor & Francis Journals, Taylor & Francis Journals, vol. 3(11), pages 701-706.
  4. Dominique, C-René & Rivera-Solis, Luis Eduardo, 2011. "Mixed fractional Brownian motion, short and long-term Dependence and economic conditions: the case of the S&P-500 Index," MPRA Paper 34860, University Library of Munich, Germany.
  5. Alvarez-Ramirez, Jose & Alvarez, Jesus & Rodriguez, Eduardo & Fernandez-Anaya, Guillermo, 2008. "Time-varying Hurst exponent for US stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 387(24), pages 6159-6169.
  6. Arneodo, A. & Bacry, E. & Muzy, J.F., 1995. "The thermodynamics of fractals revisited with wavelets," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 213(1), pages 232-275.
  7. Medio,Alfredo & Gallo,Giampaolo, 1995. "Chaotic Dynamics," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521484619.
  8. Cornelis A. Los, 2000. "Visualization of Chaos for Finance Majors," School of Economics Working Papers, University of Adelaide, School of Economics 2000-07, University of Adelaide, School of Economics.
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Cited by:
  1. Dominique, C-Rene, 2013. "Estimating investors' behavior and errorsin probabilistic forecasts by the Kolmogorov entropy and noise colors of multifractal attractors," MPRA Paper 46231, University Library of Munich, Germany, revised 16 Apr 2013.
  2. Dominique, C-Rene & Rivera-Solis, Luis Eduardo, 2012. "The dynamics of market share’s growth and competition in quadratic mappings," MPRA Paper 43652, University Library of Munich, Germany.

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