Identification of the multiscale fractional Brownian motion with biomechanical applications

Details Identification of the multiscale fractional Brownian motion with biomechanical applications Identification of the multiscale fractional Brownian motion with biomechanical applications

2007-01-30

arxiv.org/abs/math/0701873v1

Journal of Time Series Analysis 28 (01/2007) 1-52

Mathematics

Statistics Theory

Scientific paper

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.

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