Article Dans Une Revue Physica D: Nonlinear Phenomena Année : 1992

Singular-spectrum analysis: A toolkit for short, noisy chaotic signals

Résumé

Singular-spectrum analysis (SSA) is developed further, based on experience with applications to geophysical time series. It is shown that SSA provides a crude but robust approximation of strange attractors by tori, in the presence of noise. The method works well for short, noisy time series. The lagged-covariance matrix of the processes studied is the basis of SSA. We select subsets of eigenelements and associated principal components (PCs) in order to provide (i) a noise-reduction algorithm, (ii) a detrending algorithm, and (iii) an algorithm for the identification of oscillatory components. Reconstructed components (RCs) are developed to provide optimal reconstruction of a dynamic process at precise epochs, rather than averaged over the window length of the analysis. SSA is combined with advanced spectral-analysis methods - the maximum entropy method (MEM) and the multi-taper method (MTM) - to refine the interpretation of oscillatory behavior. A combined SSA-MEM method is also used for the prediction of selected subsets of RCs. The entire toolkit is validated against a set of four prescribed time series generated by known processes, quasi-periodic or chaotic. It is also applied to a time series of global surface air temperatures, 130 years long, which has attracted considerable attention in the context of the global warming issue and provides a severe test for noise reduction and prediction.

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hal-03334779 , version 1 (17-06-2025)

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Robert Vautard, Pascal Yiou, Michael Ghil. Singular-spectrum analysis: A toolkit for short, noisy chaotic signals. Physica D: Nonlinear Phenomena, 1992, 58 (1-4), pp.95-126. ⟨10.1016/0167-2789(92)90103-T⟩. ⟨hal-03334779⟩
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