Statistical study of the wavelet analysis of fractional Brownian motion

Jean Marc Bardet

doi:10.1109/18.992817

Statistical study of the wavelet analysis of fractional Brownian motion

Jean Marc Bardet

Université de Toulouse

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	991-999
Number of pages	9
Journal	IEEE Transactions on Information Theory
Volume	48
Issue number	4
DOIs	https://doi.org/10.1109/18.992817
Publication status	Published - 1 Apr 2002
Externally published	Yes

Keywords

Estimation of the self-similarity index
Fractional Brownian motion
Self-similarity
Wavelet analysis

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10.1109/18.992817

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AB - 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.

KW - Estimation of the self-similarity index

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KW - Self-similarity

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JF - IEEE Transactions on Information Theory

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Statistical study of the wavelet analysis of fractional Brownian motion

Abstract

Keywords

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