Mixed fractional Brownian motion, short and long-term Dependence and economic conditions: the case of the S&P-500 Index
AbstractThe 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 InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 34860.
Date of creation: 20 Oct 2011
Date of revision:
Publication status: Forthcoming in International Business and Management No.2.Vol.3(2011): pp. 1-13
Gaussian Processes; Mixed Fractional Brownian Motion; Hurst Exponent; Local Self-similarity; Persistence; Anti-persistence; Definiteness of covariance Functions; Dissipative dynamic systems;
Find related papers by JEL classification:
- C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
- D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
- C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-11-28 (All new papers)
- NEP-ECM-2011-11-28 (Econometrics)
- NEP-ETS-2011-11-28 (Econometric Time Series)
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