1, the greater the degree of persistence or long-range dependence. H less than 0.5 corresponds to anti-persistency, which as the opposite of LRD indicates strong negative correlation so that the process fluctuates violently. Estimation of the Hurst Parameter Slowly decaying variances, LRD, and a spectral density obeying a power-law are different manifestations of the property of the underlying covariance stationary process X. Therefore, it is possible to approach the problem of estimating the Hurst parameter from three difference angles: Variance-time plot: based on the analysis of the variances of the aggregate processes R/S statistics: based on the time-domain analysis of the rescaled adjusted range Periodogram: based on a frequency-domain analysis Relation to self-similar processes 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. In the converse, given a self-similar process with stationary increments with Hurst index H > 0.5, its increments (consecutive differences of the process) is a stationary LRD sequence. 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), while in the LRD case the self-similar process is a self-similar process with H > 0.5, the most typical one being fractional Brownian motion. Models Among stochastic models that are used for long-range dependence, some popular ones are autoregressive fractionally integrated moving average models, which are defined for discrete-time processes, while continuous-time models might start from fractional Brownian motion. See also Long-tail traffic Traffic generation model Detrended fluctuation analysis Tweedie distributions Fractal dimension Hurst exponent Notes Further reading Autocorrelation Teletraffic