Wavelet based estimator for the self-similarity parameter of /spl alpha/-stable processes

Authors:
P. Abry;L. Delbeke;P. Flandrin
Affiliations:
ENS, CNRS, Lyon, France;-;-
Venue:
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 03
Year:
1999

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Abstract

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 /spl alpha/-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.