PublicaciΓ³n:
Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics

Fecha
2021-02-11
Autores
Matilla GarcΓ­a, Mariano
Morales, Isidro
RodrΓ­guez, JosΓ© Miguel
Ruiz MarΓ­n, Manuel
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Derechos de acceso
info:eu-repo/semantics/openAccess
TΓ­tulo de la revista
ISSN de la revista
TΓ­tulo del volumen
Editor
MDPI
Proyectos de investigaciΓ³n
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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 πœβˆ— and embedding dimension p for phase space reconstruction. The value of πœβˆ— can be estimated from the Mutual Information, but this method is rather cumbersome computationally. Additionally, some researchers have recommended that πœβˆ— should be chosen to be dependent on the embedding dimension p by means of an appropriate value for the time delay πœπ‘€=(π‘βˆ’1)πœβˆ—, 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 πœπ‘€ and πœβˆ—. In this paper, we suggest a simple method for estimating πœβˆ— and πœπ‘€ based on symbolic analysis and symbolic entropy. As in the C-C method, πœβˆ— is estimated as the first local optimal time delay and πœπ‘€ 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
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
Grupo de investigaciΓ³n
Grupo de innovaciΓ³n
Programa de doctorado
CΓ‘tedra