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Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time seriesTwo dimensions of a dynamical system given by experimental time series are distinguished. Statistical dimension gives a theoretical upper bound for the minimal number of degrees of freedom required to describe the attractor up to the accuracy of the data, taking into account sampling and noise problems. The dynamical dimension is the intrinsic dimension of the attractor and does not depend on the quality of the data. Singular Spectrum Analysis (SSA) provides estimates of the statistical dimension. SSA also describes the main physical phenomena reflected by the data. It gives adaptive spectral filters associated with the dominant oscillations of the system and clarifies the noise characteristics of the data. SSA is applied to four paleoclimatic records. The principal climatic oscillations and the regime changes in their amplitude are detected. About 10 degrees of freedom are statistically significant in the data. Large noise and insufficient sample length do not allow reliable estimates of the dynamical dimension.
Document ID
19900040271
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Vautard, R.
(California Univ. Los Angeles, CA, United States)
Ghil, M.
(California, University Los Angeles, United States)
Date Acquired
August 14, 2013
Publication Date
January 1, 1989
Publication Information
Publication: Physica D - Nonlinear Phenomena
Volume: 35
ISSN: 0167-2789
Subject Category
Statistics And Probability
Accession Number
90A27326
Funding Number(s)
CONTRACT_GRANT: NSF ATM-86-15424
CONTRACT_GRANT: NAG5-713
Distribution Limits
Public
Copyright
Other

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