A practical comparison of fBm estimators

Wavelet estimator of the H parameter for fractional Brownian motion (fBm) is the most interesting one from a theoretical point of view. Indeed, Wavelet estimates are asymptotically efficient and has a complexity in only O(N). However, on limited time signals, the efficiency is not proved. In addition, some corrections have to be performed to maintain high performances. As a result, the complexity of the wavelet estimator increases so that other estimators can be thought of. In this paper, we are comparing wavelet estimator to maximum likelihood ones (classical and Whittle type) which both have also interesting theoretical properties. Results show that Whittle ML estimator is the best in terms of performances and complexity.