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Journal Article

Spike Spectra for Recurrences

Authors
/persons/resource/hkraemer

Krämer,  Kai-Hauke
Potsdam Institute for Climate Impact Research;

/persons/resource/frank.hellmann

Hellmann,  Frank
Potsdam Institute for Climate Impact Research;

/persons/resource/Mehrnaz.Anvari

Anvari,  Mehrnaz
Potsdam Institute for Climate Impact Research;

/persons/resource/Juergen.Kurths

Kurths,  Jürgen
Potsdam Institute for Climate Impact Research;

/persons/resource/Marwan

Marwan,  Norbert
Potsdam Institute for Climate Impact Research;

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Fulltext (public)

kraemer_2022_entropy-24-01689.pdf
(Publisher version), 14MB

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Citation

Krämer, K.-H., Hellmann, F., Anvari, M., Kurths, J., Marwan, N. (2022): Spike Spectra for Recurrences. - Entropy, 24, 11, 1689.
https://doi.org/10.3390/e24111689


Cite as: https://publications.pik-potsdam.de/pubman/item/item_27990
Abstract
In recurrence analysis, the τ-recurrence rate encodes the periods of the cycles of the underlying high-dimensional time series. It, thus, plays a similar role to the autocorrelation for scalar time-series in encoding temporal correlations. However, its Fourier decomposition does not have a clean interpretation. Thus, there is no satisfactory analogue to the power spectrum in recurrence analysis. We introduce a novel method to decompose the τ-recurrence rate using an over-complete basis of Dirac combs together with sparsity regularization. We show that this decomposition, the inter-spike spectrum, naturally provides an analogue to the power spectrum for recurrence analysis in the sense that it reveals the dominant periodicities of the underlying time series. We show that the inter-spike spectrum correctly identifies patterns and transitions in the underlying system in a wide variety of examples and is robust to measurement noise.