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Testing Time Series for Nonlinearity
Statistics and Computing, 2001The technique of surrogate data analysis may be employed to test the hypothesis that an observed data set was generated by one of several specific classes of dynamical system. Current algorithms for surrogate data analysis enable one, in a generic way, to test for membership of the following three classes of dynamical system: (0) independent and ...
Michael Small +2 more
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NONLINEAR TRANSFORMATIONS OF INTEGRATED TIME SERIES
Journal of Time Series Analysis, 1991Abstract. In this paper we consider the effects of nonlinear transformations on integrated processes and unit root tests performed on such series. A test that is invariant to monotone data transformations is proposed. It is shown that series are generally not cointegrated with nonlinear transformations of themselves, but the same transformation ...
Granger, C. W. J., Hallman, Jeff
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A SMOOTHING ALGORITHM FOR NONLINEAR TIME SERIES
International Journal of Bifurcation and Chaos, 2004A new NARMA based smoothing algorithm is introduced for chaotic and nonchaotic time series. The new algorithm employs a cross-validation method to determine the smoother structure, requires very little user interaction, and can be combined with wavelet thresholding to further enhance the noise reduction.
Stephen A. Billings, Kian L. Lee
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NONLINEAR TIME SERIES ANALYSIS IN EPILEPSY
International Journal of Bifurcation and Chaos, 2007The framework of the theory of nonlinear dynamics provides powerful concepts and algorithms to study complicated dynamics such as brain electrical activity (electroencephalogram, EEG). Although different influencing factors render the use of nonlinear measures in a strict sense problematic, converging evidence from various investigations now indicates
Hannes Osterhage, Klaus Lehnertz
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nonlinear time series analysis [PDF]
Since the early 1980s, there has been a growing interest in stochastic nonlinear dynamical systems of the form, where is a zero mean, covariance stationary process, is the conditional volatility, and is an independent and identically distributed noise process.
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Modeling nonlinear time series
[Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing, 1992It is argued that the ubiquity of strange attractors in nature suggests that using nonlinear modeling techniques might improve performance in some signal processing applications. A synthetic data set generated by numerically integrating a simple nonlinear differential equation is described, and the case with which crude nonlinear methods outperform ...
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Surrogate for nonlinear time series analysis
Physical Review E, 2001We present a surrogate for use in nonlinear time series analysis. This surrogate algorithm has significant advantages over the most commonly used surrogates, in that it provides a more robust statistical test by producing an entire population of surrogates that are consistent with the null hypothesis.
K T, Dolan, M L, Spano
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Series method in nonlinear time optimality
IEEE Conference on Decision and Control and European Control Conference, 2011We develop the formal series technique for analysis of the time-optimal control problem. We introduce a concept of equivalence of symmetric control systems in the sense of time optimality. Our approach is based on the consideration of a free algebra of iterated integrals and structures induced in this algebra by control systems.
Grigory M. Sklyar +1 more
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Nonlinear time series analysis of electrocardiograms
Chaos: An Interdisciplinary Journal of Nonlinear Science, 1995In recent years there has been an increasing number of papers in the literature, applying the methods and techniques of Nonlinear Dynamics to the time series of electrical activity in normal electrocardiograms (ECGs) of various human subjects. Most of these studies are based primarily on correlation dimension estimates, and conclude that the dynamics ...
A., Bezerianos +3 more
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Modelling Nonlinear Economic Time Series
2010AbstractThis book contains a up-to-date overview of nonlinear time series models and their application to modelling economic relationships. It considers nonlinear models in stationary and nonstationary frameworks, and both parametric and nonparametric models are discussed.
Terasvirta, Timo; id_orcid 0000-0002-0947-2114 +2 more
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