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

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dc.contributor.authorMatilla GarcΓ­a, Mariano
dc.contributor.authorMorales, Isidro
dc.contributor.authorRodrΓ­guez, JosΓ© Miguel
dc.contributor.authorRuiz MarΓ­n, Manuel
dc.date.accessioned2025-01-13T11:44:23Z
dc.date.available2025-01-13T11:44:23Z
dc.date.issued2021-02-11
dc.descriptionThe registered version of this article, first published in Entropy, is available online at the publisher's website: MDPI, https://doi.org/10.3390/e23020221
dc.descriptionLa 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
dc.description.abstractThe 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 episodesen
dc.description.versionversiΓ³n publicada
dc.identifier.citationMatilla-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.
dc.identifier.doihttps://doi.org/10.3390/e23020221
dc.identifier.issn1099-4300
dc.identifier.urihttps://hdl.handle.net/20.500.14468/25222
dc.journal.issue2
dc.journal.titleEntropy
dc.journal.volume23
dc.language.isoen
dc.publisherMDPI
dc.relation.centerFacultades y escuelas::Facultad de Ciencias EconΓ³micas y Empresariales
dc.relation.departmentEconomΓ­a Aplicada y EstadΓ­stica
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/deed.es
dc.subject53 Ciencias EconΓ³micas
dc.subject.keywordssymbolic analysisen
dc.subject.keywordssymbolic entropyen
dc.subject.keywordsdelay time selectionen
dc.subject.keywordsdynamic reconstructionen
dc.titleSelection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamicsen
dc.typeartΓ­culoes
dc.typejournal articleen
dspace.entity.typePublication
relation.isAuthorOfPublication7ad4a531-f3a5-451d-a646-48a1cd0ad86e
relation.isAuthorOfPublication.latestForDiscovery7ad4a531-f3a5-451d-a646-48a1cd0ad86e
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