A wavelet based estimator for the parameter of self-similarity of fractional Brownian motion

Let X be a continuous fractional Brownian motion with parameter of self-similarity H. Let \psi be a wavelet function with compact support and let \psi_{j,k} be rescaled versions of the function \psi at position k. We investigate the basic properties of the estimator for H based on wavelet coefficients D_{j,k}=\int W(t)\psi_{j,k}(t) dt. The estimator is a weighted sum of random variables which form a stationary, strongly mixing sequence. We show that the estimator is unbiased, consistent and has asymptotically a normal distribution.status: publishe