Mixed fractional Brownian motion, short and long-term Dependence and economic conditions: the case of the S&P-500 Index
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.
|Date of creation:||20 Oct 2011|
|Publication status:||Forthcoming in International Business and Management No.2.Vol.3(2011): pp. 1-13|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
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.:
- 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.
- Lobato, I.N. & Savin, N.E., 1996. "Real and Spurious Long Memory Properties of Stock Market Data," Working Papers 96-07, University of Iowa, Department of Economics.
- I.N. Lobato & N.E. Savin, 1996. "Real and Spurious Long Memory Properties of Stock Market Data," Econometrics 9605004, EconWPA, revised 26 Sep 1996.
- Joseph G. Haubrich & Andrew W. Lo, "undated". "The Sources and Nature of Long-Term Memory in the Business Cycle," Rodney L. White Center for Financial Research Working Papers 05-89, Wharton School Rodney L. White Center for Financial Research.
- Joseph G. Haubrich & Andrew W. Lo, 1991. "The sources and nature of long-term memory in the business cycle," Working Paper 9116, Federal Reserve Bank of Cleveland.
- Joseph G. Haubrich & Andrew W. Lo, "undated". "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.
- Joseph G. Haubrich & Andrew W. Lo, 1989. "The Sources and Nature of Long-term Memory in the Business Cycle," NBER Working Papers 2951, National Bureau of Economic Research, Inc.
- Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
- 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.
- Andrew W. Lo, 1989. "Long-term Memory in Stock Market Prices," NBER Working Papers 2984, National Bureau of Economic Research, Inc.
- Tom Doan, "undated". "RSSTATISTIC: RATS procedure to compute R/S Statistic (classical or Lo's modified)," Statistical Software Components RTS00191, Boston College Department of Economics.
- 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.
- 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.
- 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.
- 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. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:34860. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter)
If references are entirely missing, you can add them using this form.