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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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  • Dominique, C-Rene & Rivera-Solis, Luis Eduardo, 2012. "Short-term Dependence in Time Series as an Index of Complexity: Example from the S&P-500 Index," MPRA Paper 41408, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:41408
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    File URL: https://mpra.ub.uni-muenchen.de/41408/1/MPRA_paper_41408.pdf
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    References listed on IDEAS

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    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, vol. 16(3), pages 261-268, July.
    3. Invernizzi, Sergio & Medio, Alfredo, 1991. "On lags and chaos in economic dynamic models," Journal of Mathematical Economics, Elsevier, vol. 20(6), pages 521-550.
    4. Cornelis A. Los, 2000. "Visualization of Chaos for Finance Majors," School of Economics and Public Policy Working Papers 2000-07, University of Adelaide, School of Economics and Public Policy.
    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, vol. 387(24), pages 6159-6169.
    6. Thomas Lux, 1996. "Long-term stochastic dependence in financial prices: evidence from the German stock market," Applied Economics Letters, Taylor & Francis Journals, vol. 3(11), pages 701-706.
    7. 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.
    8. Medio,Alfredo & Gallo,Giampaolo, 1995. "Chaotic Dynamics," Cambridge Books, Cambridge University Press, number 9780521484619.
    9. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 280-283, July.
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    Citations

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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, 2018. "Could Noise Spectra of Strange Attractors Better Explained Wealth and Income Inequalities? Evidence from the S&P-500 Index," MPRA Paper 84182, University Library of Munich, Germany.
    3. 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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    More about this item

    Keywords

    Hurst Exponent; anti-persistence; fractal attractors; SDIC; chaos; inherent noise; market crashes; Renyi’s generalized fractal dimensions;
    All these keywords.

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • A1 - General Economics and Teaching - - General Economics
    • G01 - Financial Economics - - General - - - Financial Crises

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