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

26 Pages Posted: 30 May 2016  

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

H. Vincent Poor

Princeton University - Department of Electrical Engineering

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering

Date Written: December 1, 2003

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 1N. 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.

Keywords: High-frequency data, S\&P 500 index, long range dependence, heavy tailed marginals, fractional Brownian motion, wavelet analysis, log scale spectrum

Suggested Citation

Bayraktar, Erhan and Poor, H. Vincent and Sircar, Ronnie, Estimating the Fractal Dimension of the S&P 500 Index Using Wavelet Analysis (December 1, 2003). International Journal of Theoretical and Applied Finance, Vol. 7, No. 5, 2004. Available at SSRN: https://ssrn.com/abstract=2785828

Erhan Bayraktar (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

H. Vincent Poor

Princeton University - Department of Electrical Engineering ( email )

Princeton, NJ 08544
United States

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering ( email )

Princeton, NJ 08544
United States

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