Fractal dimension estimators for fractional Brownian motions

Five different fractal dimension estimators are chosen which operate either in the frequency domain (identification of a spectral exponent via spectrum analysis), in the time domain (maximum likelihood on one hand, methods based on length measurements of fractional Brownian motion samples at different observation scales on the other hand), or in a mixed time-scale domain (identification of a self-similarity parameter via the variance of wavelets coefficients). The relevance of these different estimators is discussed, and their performance is compared on simulated and real data. Performance evaluation of analysis is made difficult by the fact that there exists no unique and satisfactory synthesis method for generating such processes