Using dynamics to analyse time series

Sjoerd Verduyn Lunel

doi:10.1007/978-3-319-64173-7_20

Using dynamics to analyse time series

Sjoerd Verduyn Lunel^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

We present a review of recent work to analyze time series in a robust manner using Wasserstein distances which are numerical costs of an optimal transportation problem. Given a time series, the long-term behavior of the dynamical system represented by the time series is reconstructed by Takens delay embedding method. This results in probability distributions over phase space and to each pair we then assign a numerical distance that quantifies the differences in their dynamical properties. From the totality of all these distances a low-dimensional representation in a Euclidean space is derived. This representation shows the functional relationships between the time series under study. For example, it allows to assess synchronization properties and also offers a new way of numerical bifurcation analysis. Several examples are given to illustrate our results. This work is based on ongoing joint work with Michael Muskulus [19, 20].

Original language	English
Title of host publication	Patterns of Dynamics - In Honour of Bernold Fiedler’s 60th Birthday
Editors	Pavel Gurevich, Juliette Hell, Arnd Scheel, Bjorn Sandstede
Publisher	Springer
Pages	370-392
Number of pages	23
ISBN (Electronic)	978-3-319-64173-7
ISBN (Print)	978-3-319-64172-0
DOIs	https://doi.org/10.1007/978-3-319-64173-7_20
Publication status	Published - 8 Feb 2018
Event	Conference on Patterns of Dynamics held in honor of Bernold Fiedler’s 60th Birthday, 2016 - Berlin, Germany Duration: 25 Jul 2016 → 29 Jul 2016

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	205
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	Conference on Patterns of Dynamics held in honor of Bernold Fiedler’s 60th Birthday, 2016
Country/Territory	Germany
City	Berlin
Period	25/07/16 → 29/07/16

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG 2017.

Keywords

Attractors
Dynamical systems
Optimal transport and wasserstein distances
Synchronization
Time series analysis

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10.1007/978-3-319-64173-7_20

978-3-319-64173-7_20Final published version, 1.17 MBLicence: Taverne

Cite this

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Verduyn Lunel, S 2018, Using dynamics to analyse time series. in P Gurevich, J Hell, A Scheel & B Sandstede (eds), Patterns of Dynamics - In Honour of Bernold Fiedler’s 60th Birthday. Springer Proceedings in Mathematics and Statistics, vol. 205, Springer, pp. 370-392, Conference on Patterns of Dynamics held in honor of Bernold Fiedler’s 60th Birthday, 2016, Berlin, Germany, 25/07/16. https://doi.org/10.1007/978-3-319-64173-7_20

Using dynamics to analyse time series. / Verduyn Lunel, Sjoerd.
Patterns of Dynamics - In Honour of Bernold Fiedler’s 60th Birthday. ed. / Pavel Gurevich; Juliette Hell; Arnd Scheel; Bjorn Sandstede. Springer, 2018. p. 370-392 (Springer Proceedings in Mathematics and Statistics; Vol. 205).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Using dynamics to analyse time series

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Keywords

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