Maximum likelihood estimation of the parameters of fractional Brownian motions

This paper provides convergence analysis for maximum likelihood estimation of the parameters describing a particular multiscale process known as fractional Brownian motion. We concentrate on schemes that 'pre-whiten' the available noise-corrupted data via the fast wavelet transform and show that such schemes are strongly consistent and asymptotically efficient. We also analyse the rate of convergence of the maximum likelihood estimates and show that this rate depends on the memory of the fractional process.