Estimating the fractal dimension of the S&P 500 index using wavelet analysis

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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 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.

Original languageEnglish (US)
Pages (from-to)615-643
Number of pages29
JournalInternational Journal of Theoretical and Applied Finance
Issue number5
StatePublished - Aug 2004

All Science Journal Classification (ASJC) codes

  • General Economics, Econometrics and Finance
  • Finance


  • Fractional Brownian motion
  • Heavy tailed marginals
  • High-frequency data
  • Log scale spectrum
  • Long range dependence
  • S&P 500 index
  • Wavelet analysis


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