Statistical study of the wavelet analysis of fractional Brownian motion

Authors:
J. -M. Bardet
Affiliations:
Lab. de Statistique et Probabilite, Univ. Paul Sabatier, Toulouse
Venue:
IEEE Transactions on Information Theory
Year:
2006

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Abstract

We present a statistical study of wavelet coefficients of a fractional Brownian motion. A central limit theorem for empirical variances of exact wavelet coefficients is given. Under conditions on the mother wavelet and the choice of scales, a limit theorem is given for fitted wavelet coefficients computed from a time series. It provides an estimator for the self-similarity parameter of Gaussian time series