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Phase correlations in nonlinear time series analysis

Modest, Heike and Räth, Christoph and Schreiber, Korbinian (2016) Phase correlations in nonlinear time series analysis. 14th Experimental Chaos and Complexity Conference, 16.-19- Mai 2016, Banff, Canada. (Unpublished)

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Abstract

Nonlinear times series properties are represented by the Fourier phases of the time series and for a comprehensive description of nonlinear data it is necessary to include the quantification of Fourier phase information. We introduce a novel method that traces nonlinearities by detecting correlations among the Fourier phases. The basic idea of the so-called phase walk statistics (PWS) is to measure - in close analogy to random walks - the deviation from randomness of the unwrapped differences of phases. The method compares distributions of phases from experimental and simulated time series with distributions that follow the null hypothesis of having totally random and uniformly distributed steps. It is shown that the obtained signifcances of nonlinear influence are comparable to those of well established measures. However, the results are obtained with orders of magnitude less computational effort, enabling much refined statistical analyses. We point out that the method can even identify specific scales on which nonlinear effects occur - a feature, not yet reached by any conventional method. A surrogate assisted analysis further shows that PWS is able to disentangle different classes of nonlinearities which have indistinguishable PDFs. The presented algorithms can be used to quantify nonlinear influence on time series of any physical, biological or financial system. We demonstrate the performance of the new approach via examples from Econophysics (Dow Jones time series), Plasmaphysics (trajectories of dust particles in vortices) and Aerodynamics (wind data with intermittencies).

Item URL in elib:https://elib.dlr.de/109596/
Document Type:Conference or Workshop Item (Speech)
Title:Phase correlations in nonlinear time series analysis
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Modest, HeikeHeike.Modest (at) dlr.deUNSPECIFIED
Räth, ChristophChristoph.Raeth (at) dlr.deUNSPECIFIED
Schreiber, KorbinianKorbinian.Schreiber (at) dlr.deUNSPECIFIED
Date:18 May 2016
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Status:Unpublished
Keywords:nonlinear data analysis, phase statistics, time series
Event Title:14th Experimental Chaos and Complexity Conference
Event Location:Banff, Canada
Event Type:international Conference
Event Dates:16.-19- Mai 2016
Organizer:University of Calgary
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Space
HGF - Program Themes:Research under Space Conditions
DLR - Research area:Raumfahrt
DLR - Program:R FR - Forschung unter Weltraumbedingungen
DLR - Research theme (Project):R - Komplexe Plasmen / Data analysis, R - Komplexe Plasmen / Theory, Simulation
Location: Oberpfaffenhofen
Institutes and Institutions:Research Group Complex Plasma
Deposited By: Modest, Heike
Deposited On:15 Dec 2016 10:24
Last Modified:15 Dec 2016 10:24

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