Koltai, Péter and Kunde, Philipp
(2024)
*A Koopman-Takens theorem: Linear least squares prediction of nonlinear time series.*
Preprint
.
(In Press)

Full text not available from this repository.

Official URL: https://doi.org/10.48550/arXiv.2308.02175

## 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.

Item Type: | Article |
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Subjects: | Mathematical and Computer Sciences Mathematical and Computer Sciences > Mathematics Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 3134 |

Deposited By: | Lukas-Maximilian Jaeger |

Deposited On: | 03 Apr 2024 09:30 |

Last Modified: | 04 Apr 2024 10:34 |

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