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Title: Detecting determinism in time series : the method of surrogate data
Authors: Small, M
Tse, CKM 
Issue Date: May-2003
Source: IEEE transactions on circuits and systems. I, Fundamental theory and applications, May 2003, v. 50, no. 5, p. 663-672
Abstract: We review a relatively new statistical test that may be applied to determine whether an observed time series is inconsistent with a specific class of dynamical systems. These surrogate data methods may test an observed time series against the hypotheses of: i) independent and identically distributed noise; ii) linearly filtered noise; and iii) a monotonic nonlinear transformation of linearly filtered noise. A recently suggested fourth algorithm for testing the hypothesis of a periodic orbit with uncorrelated noise is also described. We propose several novel applications of these methods for various engineering problems, including: identifying a deterministic (message) signal in a noisy time series; and separating deterministic and stochastic components. When employed to separate deterministic and noise components, we show that the application of surrogate methods to the residuals of nonlinear models is equivalent to fitting that model subject to an information theoretic model selection criteria.
Keywords: Hypothesis testing
Minimum description length
Noise separation
Nonlinear modeling
Surrogate data
Publisher: Institute of Electrical and Electronics Engineers
Journal: IEEE transactions on circuits and systems. I, Fundamental theory and applications 
ISSN: 1057-7122
DOI: 10.1109/TCSI.2003.811020
Rights: © 2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
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