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Data-adaptive wavelets and multi-scale singular-spectrum analysis期刊论文

作者: Yiou Pascal Sornette Didier Ghil Michael
DOI:10.1016/S0167-2789(00)00045-2

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页码: 254-290
被引频次: 79
出版者: Elsevier B.V,ELSEVIER SCIENCE BV
ISSN: 0167-2789
卷期: Volume:142    Issue:3
语言: English
摘要: Using multi-scale ideas from wavelet analysis, we extend singular-spectrum analysis (SSA) to the study of nonstationary time series, including the case where intermittency gives rise to the divergence of their variance. The wavelet transform resembles a local Fourier transform within a finite moving window whose width W, proportional to the major period of interest, is varied to explore a broad range of such periods. SSA, on the other hand, relies on the construction of the lag-correlation matrix C on M lagged copies of the time series over a fixed window width W to detect the regular part of the variability in that window in terms of the minimal number of oscillatory components; here W = M Δt with Δt as the time step. The proposed multi-scale SSA is a local SSA analysis within a moving window of width M ≤ W ≤ N, where N is the length of the time series. Multi-scale SSA varies W, while keeping a fixed W/M ratio, and uses the eigenvectors of the corresponding lag-correlation matrix C as data-adaptive wavelets; successive eigenvectors of C correspond approximately to successive derivatives of the first mother wavelet in standard wavelet analysis. Multi-scale SSA thus solves objectively the delicate problem of optimizing the analyzing wavelet in the time-frequency domain by a suitable localization of the signal's correlation matrix. We present several examples of application to synthetic signals with fractal or power-law behavior which mimic selected features of certain climatic or geophysical time series. The method is applied next to the monthly values of the Southern Oscillation Index (SOI) for 1933-1996; the SOI time series is widely believed to capture major features of the El Niño/Southern Oscillation (ENSO) in the Tropical Pacific. Our methodology highlights an abrupt periodicity shift in the SOI near 1960. This abrupt shift between 5 and 3 years supports the Devil's staircase scenario for the ENSO phenomenon (preliminary results of this study were presented at the XXII General Assembly of the European Geophysical Society, Vienna, May 1997, and at the Fall Meeting of the American Geophysical Union, San Francisco, December 1997). © 2000 Elsevier Science B.V. All rights reserved.
相关主题: Wavelets, Climatic signals, Singular-spectrum analysis, EL Niño/Southern Oscillation, Nonstationary time series, BOOLEAN DELAY EQUATIONS, INTERDECADAL VARIABILITY, PHYSICS, MULTIDISCIPLINARY, climatic signals, OCEAN-ATMOSPHERE MODEL, HIERARCHICAL-MODELS, COLORED NOISE, MONTE-CARLO SSA, SEASONAL CYCLE, PHYSICS, MATHEMATICAL, EL Nino/Southern oscillation, singular-spectrum analysis, nonstationary time series, wavelets, DATA ASSIMILATION, NINO SOUTHERN OSCILLATION, EL-NINO,

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