Nonlinear Time Series Analysis

By Holger Kantz, Thomas Schreiber. 2005

2,910 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/efdb1732e62b8619d03ef9c00a1e292dc5213dfa

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In Artificial Intelligence

Citations in the corpus

Data Based Identification and Prediction of Nonlinear and Complex Dynamical Systems (2016, methodology): “ theoretic measure, the causation entropy, was also proposed [318–320]. Convergent cross mapping framework (CCM) is based on delay coordinate embedding, the paradigm of nonlinear time series analysis [43,44,60,321]. The CCM method can deal with both linear and nonlinear systems with small data sets,”
Transfer entropy—a model-free measure of effective connectivity for the neurosciences (2010, background): “While there is an extensive literature on how to choose such parameters, the different methods proposed are far away from reaching any consensus (Kantz and Schreiber 1997).”
HERMES: Towards an Integrated Toolbox to Characterize Functional and Effective Brain Connectivity (2013, methodology): “This type of tests offers an intuitive and powerful nonparametric framework for the statistical analysis of connectivity measures (as well as signal amplitude measures, power spectra, etc.) that accounts for the inherent multiplicity involved in the statistical testing.”
Wavelet networks: an alternative to classical neural networks (2005, methodology): “One thousand data points are generated using equations (6) and (7).”
JIDT: An Information-Theoretic Toolkit for Studying the Dynamics of Complex Systems (2014, methodology): “Several bias correction techniques are available, e.g. [109, 110], though not yet implemented in JIDT.”
Predicting monthly streamflow using data‐driven models coupled with data‐preprocessing techniques (2009, background): “[17 ]T het can be defined when the autocorrelation function (ACF) attains the value of zero or below a small value, or the average mutual information (AMI) reaches the first minimum [Tsonis, 1992; Kantz and Schreiber, 2004 ].”
Suitability of Dysphonia Measurements for Telemonitoring of Parkinson's Disease (2008, methodology): “2) Calculation of Nonstandard Measures: The correlation dimension (D2) is calculated by first time-delay embedding the signal to recreate the phase space of the nonlinear dynamical system that is proposed to generate the speech signal [ 12 ].”
Vibration-based damage detection in plates by using time series analysis (2008, methodology): “The time lag DT was found using the first minimum of the average mutual information in order to generate a number of ‘‘uncorrelated’’ points in the state space [16–18].”
Cross recurrence plot based synchronization of time series (2002, positive): “The recurrence of states is a fundamental property of deterministic dynamical systems (Argyris et al., 1994; Casdagli, 1997; Kantz and Schreiber, 1997).”
Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics (2019, background): “This implies that the dynamics of the system are deterministically reconstructed in the phase space (Kantz and Schreiber, 1997) and that there exists a phase space forecasting rule zt+1 = z(zt), and thus an observable forecasting rule ôt+1 = (ot,ot− ,.”