Journal ArticleDOI
Improved Surrogate Data for Nonlinearity Tests.
Thomas Schreiber,Andreas Schmitz +1 more
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TLDR
It is shown that nonlinear rescalings of a Gaussian linear stochastic process cannot be accounted for by a simple amplitude adjustment of the surrogates which leads to spurious detection of nonlinearity.Abstract:
Current tests for nonlinearity compare a time series to the null hypothesis of a Gaussian linear stochastic process. For this restricted null assumption, random surrogates can be constructed which are constrained by the linear properties of the data. We propose a more general null hypothesis allowing for nonlinear rescalings of a Gaussian linear process. We show that such rescalings cannot be accounted for by a simple amplitude adjustment of the surrogates which leads to spurious detection of nonlinearity. An iterative algorithm is proposed to make appropriate surrogates which have the same autocorrelations as the data and the same probability distribution.read more
Citations
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Extreme value statistics in records with long-term persistence.
TL;DR: It is found numerically that the integrated distribution function of the maxima converges to a Gumbel distribution for large R similar to uncorrelated signals, and that conditional mean maxima and conditional maxima distributions should be considered for an improved extreme event prediction.
Journal ArticleDOI
From moonlight to movement and synchronized randomness: Fourier and wavelet analyses of animal location time series data
Leo Polansky,George Wittemyer,George Wittemyer,Paul C. Cross,Craig J. Tambling,Wayne M. Getz,Wayne M. Getz +6 more
TL;DR: It is proposed that frequency and time-frequency domain methods, embodied by Fourier and wavelet transforms, can serve as useful probes in early investigations of animal movement data, stimulating new ecological insight and questions and guiding appropriately flexible probabilistic models connecting movement with biotic and abiotic covariates.
Journal ArticleDOI
Testing for nonlinearity of streamflow processes at different timescales
TL;DR: In this paper, the authors investigated the character and type of nonlinearity that are present in the streamflow dynamics at different time scales (i.e. one year, one month, 1/3 month and one day).
Journal ArticleDOI
Bearing condition diagnosis and prognosis using applied nonlinear dynamical analysis of machine vibration signal
TL;DR: A modified form of the correlation integral developed by Grassberger and Procaccia referred to as the partial correlation integral, which can be computed in real time is introduced, which is used to analyze machine vibration data obtained throughout a life test of a rolling element bearing.
Journal ArticleDOI
Neuronal assembly detection and cell membership specification by principal component analysis.
Vítor Lopes-dos-Santos,Vítor Lopes-dos-Santos,Sergio A. Conde-Ocazionez,Sergio A. Conde-Ocazionez,Miguel A. L. Nicolelis,Miguel A. L. Nicolelis,Sidarta Ribeiro,Sidarta Ribeiro,Adriano B. L. Tort,Adriano B. L. Tort +9 more
TL;DR: Application of the PCA method to multielectrode recordings of awake and behaving rats revealed that assemblies detected in the cerebral cortex and hippocampus typically contain overlapping neurons, indicating that the method is able to properly detect, track and specify neuronal assemblies, irrespective of overlapping membership.
References
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Book
Time Series Prediction: Forecasting The Future And Understanding The Past
TL;DR: By reading time series prediction forecasting the future and understanding the past, you can take more advantages with limited budget.
Book
Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence
TL;DR: In this paper, the changing structure of stock returns nonlinearity in foreign exchange summary, relation to other work, and future horizons are discussed, as well as the size and distribution of the BDS statistic quantiles.
Journal ArticleDOI
Constrained-realization Monte-Carlo method for hypothesis testing
TL;DR: The typical-realization approach, on the other hand, does not share this requirement, and can provide an accurate and powerful test without having to sacrifice flexibility in the choice of discriminating statistic, and is found to depend on whether or not the discriminating statistic is pivotal.