EVALUATING SCALED WINDOWED VARIANCE METHODS FOR ESTIMATING THE HURST COEFFICIENT OF TIME-SERIES

Three-scaled windowed variance methods (standard, linear regression de trended, and bridge detrended) for estimating the Hurst coefficient (H I are evaluated. The Hurst coefficient, with 0 < H < 1, characterizes self-similar decay in the time-series autocorrelation Function. The sc aled windowed variance methods estimate H for fractional Brownian moti on (fBm) signals which are cumulative sums of fractional Gaussian nois e (fGn) signals. For all three methods both the bias and standard devi ation of estimates are less than 0.05 for series having N greater than or equal to 2(9) points. Estimates for short series (N < 2(8)) are un reliable. To have a 0.95 probability of distinguishing between two sig nals with true H differing by 0.1, more than 2(15) points are needed. All three methods proved more reliable (based on bias and variance of estimates) than Hurst's rescaled range analysis, periodogram analysis, and autocorrelation analysis. and as reliable as dispersional analysi s. The latter methods can only be applied to fGn or differences of fBm . while the scaled windowed variance methods must be applied to fBm or cumulative sums of fGn.