  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.
