A second way of characterizing long- and short-range dependence is in terms of the variance of partial sum of consecutive values.
The Hurst parameter H is a measure of the extent of long-range dependence in a time series (while it has another meaning in the context of self-similar processes).
Slowly decaying variances, LRD, and a spectral density obeying a power-law are different manifestations of the property of the underlying covariance of a stationary process.
Therefore, it is possible to approach the problem of estimating the Hurst parameter from three difference angles: Given a stationary LRD sequence, the partial sum if viewed as a process indexed by the number of terms after a proper scaling, is a self-similar process with stationary increments asymptotically, the most typical one being fractional Brownian motion.
This also holds true if the sequence is short-range dependent, but in this case the self-similar process resulting from the partial sum can only be Brownian motion (H = 0.5).