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Abstract: 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. A natural wavelet based generalisation to traditional aggregation is then proposed: "a-aggregation". It is... (Update)
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BibTeX entry: (Update)
Abry, P., Veitch, D. and Flandrin, P. (1998) Long-range Dependence: Revisiting Aggregation with Wavelets. Journal of Time Series Analysis, 19, 253--66. http://citeseer.ist.psu.edu/abry98longrange.html More
@article{ abry98long,
author = "Patrice Abry and Darryl Veitch and Patrick Flandrin",
title = "Long Range Dependence: {R}evisiting Aggregation with Wavelets",
journal = "Journal of Time Series Analysis",
volume = "19",
number = "3",
pages = "253--266",
year = "1998",
url = "citeseer.ist.psu.edu/abry98longrange.html" }
Citations (may not include all citations):1526 Ten Lectures on Wavelets (context) - Daubechies - 1992
692 the self similar nature of Ethernet traffic - Leland, Taqqu et al. - 1994
304 Statistics for Long-Memory Processes (context) - Beran - 1994
220 A storage model with self-similar input - Norros - 1994
190 Experimental Queueing Analysis with Long-Range Dependent Pac.. - Erramilli, Narayan et al. - 1996
149 Long-range dependence: a review (context) - Cox - 1984
124 Stable Non-Gaussian random Processes (context) - Samorodnitsky, Taqqu - 1994
104 Wavelet Analysis of Long Range dependent Traffic - Abry, Veitch - 1996
94 Wavelet analysis and synthesis of fractional Brownian motion (context) - Flandrin - 1992
92 Estimators for Long-Range Dependence: an Empirical Study - Taqqu, Teverovsky et al. - 1996
40 A family of polynomial spline wavelet transforms (context) - Unser, Aldroubi et al. - 1993
25 Families of multiresolution and wavelet spaces with optimal .. (context) - Aldroubi, Unser - 1993
20 Semi-parametric analysis of long-memory time-series (context) - Robinson - 1994
18 the continuous wavelet transform of second-order random proc.. (context) - Cambanis, Houdr'e - 1995
12 Lectures Note in Statistics (context) - Abry, Gon et al. - 1995
12 The wavelet transform of stochastic processes with stationar.. (context) - Masry - 1993
12 Designing Multiresolution Analysis-type Wavelets and their F.. (context) - Abry, Aldroubi - 1995
8 Statistics of atomic frequency standards (context) - Allan - 1996
4 Point-processes, Long-Range Dependence and Wavelets (context) - Abry, Flandrin - 1996
1 Veitch - Heavy Traffic Analysis of a Storage Model with Long.. (context) - Brichet, Roberts et al. - 1996
1 Wavelet-based joint estimation for the Long-range dependence.. (context) - Veitch, Abry - 1996
1 private communication (context) - Taqqu - 1996
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