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Estimating the Fractal Dimension of the S&P 500 Index using Wavelet Analysis

Author Info

• Erhan Bayraktar
• H. Vincent Poor
• Ronnie Sircar

Abstract

S&P 500 index data sampled at one-minute intervals over the course of 11.5 years (January 1989- May 2000) is analyzed, and in particular the Hurst parameter over segments of stationarity (the time period over which the Hurst parameter is almost constant) is estimated. An asymptotically unbiased and efficient estimator using the log-scale spectrum is employed. The estimator is asymptotically Gaussian and the variance of the estimate that is obtained from a data segment of $N$ points is of order $\frac{1}{N}$. Wavelet analysis is tailor made for the high frequency data set, since it has low computational complexity due to the pyramidal algorithm for computing the detail coefficients. This estimator is robust to additive non-stationarities, and here it is shown to exhibit some degree of robustness to multiplicative non-stationarities, such as seasonalities and volatility persistence, as well. This analysis shows that the market became more efficient in the period 1997-2000.

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File URL: http://arxiv.org/pdf/math/0703834
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number math/0703834.

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 Length: Date of creation: Mar 2007 Publication status: Published in International Journal of theoretical and Applied Finance, Volume 7 (5), 2004 Handle: RePEc:arx:papers:math/0703834 Contact details of provider: Web page: http://arxiv.org/

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1. Hall, Peter & Härdle, Wolfgang & Kleinow, Torsten & Schmidt, Peter, 1999. "Semiparametric bootstrap approach to hypothesis tests and confidence intervals for the hurst coefficient," SFB 373 Discussion Papers 1999,62, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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8. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
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