  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.
