Identification of the multiscale fractional Brownian motion with biomechanical applications

Jean-Marc Bardet (1, 2) , Pierre, Raphael Bertrand (3)

1 SAMOS - Statistique Appliquée et MOdélisation Stochastique
2 CES - Centre d'économie de la Sorbonne
3 PAS

In certain applications, for instance biomechanics, turbulence, finance, or Internet traffic, it seems suitable to model the data by a generalization of a fractional Brownian motion for which the Hurst parameter $H$ is depending on the frequency as a piece-wise constant function. These processes are called multiscale fractional Brownian motions. In this contribution, we provide a statistical study of the multiscale fractional Brownian motions. We develop a method based on wavelet analysis. By using this method, we find initially the frequency changes, then we estimate the different parameters and afterwards we test the goodness-of-fit. Lastly, we give the numerical algorithm. Biomechanical data are then studied with these new tools.

Mots clés: Biomechanics; Detection of change; Goodness-of-fit test; Fractional Brownian motion; Semi-parametric estimation; Wavelet analysis.; Wavelet analysis

Domaines: Statistiques [math.ST]

Jean-Marc Bardet, Pierre, Raphael Bertrand. Identification of the multiscale fractional Brownian motion with biomechanical applications. Journal of Time Series Analysis, 2007, 28 (1), pp.1-52. ⟨10.1111/j.1467-9892.2006.00494.x⟩. ⟨hal-00127953⟩