Comparison of various estimators in simulated FGN

The Hurst parameter is the simplest numerical characteristic of self-similar long-range dependent stochastic processes. Such processes have been identified in many natural and man-made systems. In particular, since they were discovered in the Internet and other multimedia telecommunication networks a decade ago, they have been the subject of numerous investigations. Typical quantitative assessment of self-similarity and long-range dependency, begins with the estimation of the Hurst parameter H. There have been a number of techniques proposed for this. This paper reports results of a comparative analysis of the six most frequently used estimators of H. To set up a credible framework for this, the minimal acceptable sample size is first determined. The Hurst parameter estimators are then compared for bias and variance. Our experimental results have confirmed that the Abry–Veitch Daubechies Wavelet-Based (DWB) and the Whittle ML (Maximum Likelihood) estimators of H are the least biased. However, the latter has significantly smaller variance and can be applied to shorter data samples than the Abry–Veitch DWB estimator. On the other hand, the Abry–Veitch DWB estimator is computationally simpler and faster than the Whittle ML estimator.