PublicaciΓ³n: Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics
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2021-02-11
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info:eu-repo/semantics/openAccess
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MDPI
Resumen
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 πβ
and embedding dimension p for phase space reconstruction. The value of πβ can be estimated from the Mutual Information, but this method is rather cumbersome computationally. Additionally, some researchers have recommended that πβ should be chosen to be dependent on the embedding dimension p by means of an appropriate value for the time delay ππ€=(πβ1)πβ, 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 ππ€ and πβ. In this paper, we suggest a simple method for estimating πβ and ππ€ based on symbolic analysis and symbolic entropy. As in the C-C method, πβ is estimated as the first local optimal time delay and ππ€ 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
DescripciΓ³n
The registered version of this article, first published in Entropy, is available online at the publisher's website: MDPI, https://doi.org/10.3390/e23020221
La versiΓ³n registrada de este artΓculo, publicado por primera vez en Entropy, estΓ‘ disponible en lΓnea en el sitio web del editor: MDPI, https://doi.org/10.3390/e23020221
La versiΓ³n registrada de este artΓculo, publicado por primera vez en Entropy, estΓ‘ disponible en lΓnea en el sitio web del editor: MDPI, https://doi.org/10.3390/e23020221
CategorΓas UNESCO
Palabras clave
symbolic analysis, symbolic entropy, delay time selection, dynamic reconstruction
CitaciΓ³n
Matilla-GarcΓa, M., Morales, I., RodrΓguez, J. M., & Ruiz MarΓn, M. (2021). Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics. Entropy, 23(2), 221.
Centro
Facultades y escuelas::Facultad de Ciencias EconΓ³micas y Empresariales
Departamento
EconomΓa Aplicada y EstadΓstica