Wavelet based estimator for the self-similarity parameter of α-stable processes

We, study self-similar processes with possibly infinite second order statistics and long-range dependence. To do so, we detail the statistical properties of the wavelet coefficients of α-stable self similar processes, used as a paradigm for those situations. We, then, propose a wavelet based estimator for the self-similarity parameter and analyse its statistical performance both theoretically and numerically. We show that it is unbiased, that its variance decreases as the inverse of the length of the data and that it can be easily implemented