ESTIMATING THE FRACTAL DIMENSION OF THE S&P 500 INDEX USING WAVELET ANALYSIS

Erhan Bayraktar, H. Vincent Poor () and K. Ronnie Sircar ()
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H. Vincent Poor: Department of Electrial Engineering, Princeton University, Princeton, NJ 08544, USA
K. Ronnie Sircar: Department of Operations Research & Financial Engineering, Princeton University, E-Quad, Princeton, NJ 08544, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2004, vol. 07, issue 05, 615-643

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 ofNpoints 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 suggests 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 (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (19)

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Working Paper: Estimating the Fractal Dimension of the S&P 500 Index using Wavelet Analysis (2007)
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DOI: 10.1142/S021902490400258X

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