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Zbl 0910.62080
Abry, Patrice; Veitch, Darryl; Flandrin, Patrick
Long-range dependence: revisiting aggregation with wavelets. (English)
[J] J. Time Ser. Anal. 19, No.3, 253-266 (1998). ISSN 0143-9782; ISSN 1467-9892/e

Summary: The aggregation procedure is a natural way to analyse signals which exhibit long-range-dependent features and has been used as a basis for estimation of the Hurst parameter, $H$. In this paper it is shown how aggregation can be naturally rephrased within the wavelet transform framework, being directly related to approximations of the signal in the sense of a Haar multiresolution analysis.\par A natural wavelet-based generalization to traditional aggregation is then proposed: `a-aggregation'. It is shown that a-aggregation cannot lead to good estimators of $H$, and so a new kind of aggregation, `d-aggregation', is defined, which is related to the details rather than the approximations of a multiresolution analysis. An estimator of $H$ based on d-aggregation has excellent statistical and computational properties, whilst preserving the spirit of aggregation. The estimator is applied to telecommunications network data.

MSC 2000:: *62M10 Time series, etc. (statistics)
42C40 Wavelets

Keywords: long-range dependence; self-similarity; wavelet transform; second order stationary process; aggregation; multiresolution analysis

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