scholarly journals Multivariate chaotic time series phase space reconstruction based on extending dimension by conditional entropy

2011 ◽  
Vol 60 (2) ◽  
pp. 020508
Author(s):  
Zhang Chun-Tao ◽  
Ma Qian-Li ◽  
Peng Hong ◽  
Jiang You-Yi
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Conditional Entropy ◽  
Phase Space Reconstruction ◽  
Chaotic Time Series

scholarly journals Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 221
Author(s):  
Mariano Matilla-García ◽  
Isidro Morales ◽  
Jose Miguel Rodríguez ◽  
Manuel Ruiz Marín
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Phase Space ◽  
Mutual Information ◽  
Phase Space Reconstruction ◽  
Chaotic Time Series ◽  
Optimal Time ◽  
Embedding Dimension ◽  
Simple Method ◽  
Correlation Integral

The modeling and prediction of chaotic time series require proper reconstruction of the state space from the available data in order to successfully estimate invariant properties of the embedded attractor. Thus, one must choose appropriate time delay τ∗ and embedding dimension p for phase space reconstruction. The value of τ∗ can be estimated from the Mutual Information, but this method is rather cumbersome computationally. Additionally, some researchers have recommended that τ∗ should be chosen to be dependent on the embedding dimension p by means of an appropriate value for the time delay τw=(p−1)τ∗, which is the optimal time delay for independence of the time series. The C-C method, based on Correlation Integral, is a method simpler than Mutual Information and has been proposed to select optimally τw and τ∗. In this paper, we suggest a simple method for estimating τ∗ and τw based on symbolic analysis and symbolic entropy. As in the C-C method, τ∗ is estimated as the first local optimal time delay and τw as the time delay for independence of the time series. The method is applied to several chaotic time series that are the base of comparison for several techniques. The numerical simulations for these systems verify that the proposed symbolic-based method is useful for practitioners and, according to the studied models, has a better performance than the C-C method for the choice of the time delay and embedding dimension. In addition, the method is applied to EEG data in order to study and compare some dynamic characteristics of brain activity under epileptic episodes

scholarly journals Hidden Phase Space Reconstruction: A Novel Chaotic Time Series Prediction Method for Speech Signals

2018 ◽  
Vol 27 (6) ◽  
pp. 1221-1228 ◽  
Author(s):  
Jingjing Li ◽  
Qijin Zhang ◽  
Yumei Zhang ◽  
Xiaojun Wu ◽  
Xiaoming Wang ◽  
...  
Keyword(s):  
Time Series ◽  
Phase Space ◽  
Time Series Prediction ◽  
Prediction Method ◽  
Phase Space Reconstruction ◽  
Chaotic Time Series ◽  
Speech Signals ◽  
Chaotic Time Series Prediction
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