The asymptotic behavior of the R/S statistic for fractional Brownian motion

This paper provides a proof of the fact that asymptotically the R/S statistic and the self-similarity index of fractional Brownian motion agree in the expectation sense. In particular for fractional Gaussian noise time series, the R/S statistic is an estimator of the self-similarity index HH. We also show that two other methods for estimating HH yield consistent estimators.