Méthodes d'analyse du mouvement brownien fractionnaire : théorie et résultats comparatifs Analysis methods for fractional brownian motion: theory and comparative results

and key words In this paper, several analysis methods for fractional Brownian motion are studied using reference test signals generated by the Cholesky procedure. Several sets of 100 signals having sample size ranging from N =3 2to 1024 by power of 2 are generated for H = 0.1 to 0.9 by steps of 0.1. Analysis techniques of the H parameter among the most well known in signal processing are studied. They are grouped in four categories: frequency based methods, geometrical methods, time methods, and multi-resolution methods. Quality of these estimators is assessed in terms of bias and variance. The variance is compared to the Cramer-Rao lower bound (CRLB). Statistical tests show that only the maximum likelihood estimator (MLE) is efficient (unbiased and reaches the CRLB) for every H and N tes- ted. This experimental result about the efficiency of MLE extends that demonstrated by Dahlhaus only in the

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