dc.contributor.author
Koltai, Péter
dc.contributor.author
Kunde, Philipp
dc.date.accessioned
2024-05-07T10:11:40Z
dc.date.available
2024-05-07T10:11:40Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/43472
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-43189
dc.description.abstract
The least squares linear filter, also called the Wiener filter, is a popular tool to predict the next element(s) of time series by linear combination of time-delayed observations. We consider observation sequences of deterministic dynamics, and ask: Which pairs of observation function and dynamics are predictable? If one allows for nonlinear mappings of time-delayed observations, then Takens’ well-known theorem implies that a set of pairs, large in a specific topological sense, exists for which an exact prediction is possible. We show that a similar statement applies for the linear least squares filter in the infinite-delay limit, by considering the forecast problem for invertible measure-preserving maps and the Koopman operator on square-integrable functions.
en
dc.format.extent
35 Seiten
dc.rights.uri
https://creativecommons.org/licenses/by/4.0/
dc.subject
Koopman–Takens Theorem
en
dc.subject
Linear Least Squares Prediction
en
dc.subject
Nonlinear Time Series
en
dc.subject.ddc
500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik
dc.title
A Koopman–Takens Theorem: Linear Least Squares Prediction of Nonlinear Time Series
dc.type
Wissenschaftlicher Artikel
dcterms.bibliographicCitation.articlenumber
120
dcterms.bibliographicCitation.doi
10.1007/s00220-024-05004-8
dcterms.bibliographicCitation.journaltitle
Communications in Mathematical Physics
dcterms.bibliographicCitation.number
5
dcterms.bibliographicCitation.volume
405
dcterms.bibliographicCitation.url
https://doi.org/10.1007/s00220-024-05004-8
refubium.affiliation
Mathematik und Informatik
refubium.affiliation.other
Institut für Mathematik
![This authority value has been confirmed as accurate by an interactive user](/cache_202e45ad85b55efaeb29160f63cd3f3b/themes/FuCD/images/authority_control/invisible.gif)
refubium.funding
Springer Nature DEAL
refubium.note.author
Die Publikation wurde aus Open Access Publikationsgeldern der Freien Universität Berlin gefördert.
refubium.resourceType.isindependentpub
no
dcterms.accessRights.openaire
open access
dcterms.isPartOf.eissn
1432-0916