A Koopman-Takens theorem : Linear least squares prediction of nonlinear time series

Title data

Koltai, Peter ; Kunde, Philipp:
A Koopman-Takens theorem : Linear least squares prediction of nonlinear time series.
arXiv , 2023
DOI: https://doi.org/10.48550/arXiv.2308.02175

Official URL:

Abstract in another language

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.

Further data

Item Type:	Preprint, postprint
Institutions of the University:	Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Dynamical Systems and Data > Chair Dynamical Systems and Data - Univ.-Prof. Dr. Peter Koltai
Result of work at the UBT:	Yes
DDC Subjects:	500 Science > 510 Mathematics
Date Deposited:	29 Aug 2023 06:11
Last Modified:	29 Aug 2023 06:11
URI:	https://eref.uni-bayreuth.de/id/eprint/86695