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Mixed fractional Brownian motion, short and long-term Dependence and economic conditions: the case of the S&P-500 Index

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

Abstract

The Kolmogorov-Mandelbrot-van Ness Process is a zero mean Gaussian process indexed by the Hurst Parameter (H). When it models financial data, a controversy arises as to whether or not financial data exhibit short or long-range dependence. This paper argues that the Mixed Fractional Brownian is a more suitable tool for the purpose as it leaves no room for controversy. It is used here to model the S&P-500 Index, sampled daily over the period 1950-2011. The main results are as follows: The S&P-500 Index is characterized by both short and long-term dependence. More explicitly, it is characterized by at least 12 distinct scaling pa-rameters that are, ex hypothesis, determined by investors’ approach to the market. When the market is dominated by “blue-chippers” or ‘long-termists’, or when bubbles are ongoing, the index is persistent; and when the market is dominated by “con-trarians”, the index jumps to anti-persistence that is a far-from-equilibrium state in which market crashes are likely to occur.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 34860.

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Date of creation: 20 Oct 2011
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Publication status: Forthcoming in International Business and Management No.2.Vol.3(2011): pp. 1-13
Handle: RePEc:pra:mprapa:34860

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Keywords: Gaussian Processes; Mixed Fractional Brownian Motion; Hurst Exponent; Local Self-similarity; Persistence; Anti-persistence; Definiteness of covariance Functions; Dissipative dynamic systems;

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  1. Lo, Andrew W. (Andrew Wen-Chuan), 1989. "Long-term memory in stock market prices," Working papers 3014-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  2. Joseph G. Haubrich & Andrew W. Lo, . "The Sources and Nature of Long-Term Memory in the Business Cycle," Rodney L. White Center for Financial Research Working Papers 5-89, Wharton School Rodney L. White Center for Financial Research.
  3. 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 261-68, July.
  4. Dominique, C-Rene & Rivera-Solis, Luis Eduardo & Des Rosiers, Francois, 2010. "Determining The Value-at-risk In The Shadow Of The Power Law: The Case Of The SP-500 Index," MPRA Paper 22604, University Library of Munich, Germany.
  5. Cheung, Yin-Wong, 1993. "Long Memory in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 93-101, January.
  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. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
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Cited by:
  1. 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.
  2. Dominique, C-Rene & Rivera-Solis, Luis Eduardo, 2012. "Could Investors’ Expectations Explain Temporal Variations in Hurst’s Exponent, Loci of Multifractal Spectra, and Statistical Prediction Errors? The Case of the S&P 500 Index," MPRA Paper 41407, University Library of Munich, Germany, revised 26 Feb 2012.

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