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Phase walk analysis of leptokurtic time series

Räth, Christoph and Modest, Heike and Schreiber, Korbinian (2019) Phase walk analysis of leptokurtic time series. DPG Frühjahrestagung, 1.-5. April 2019, Regensburg. (Unpublished)

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Abstract

A very general definition of nonlinearity in data sets can be obtained from their representation in Fourier space: From the Wiener-Khintchine theorem and the bijectivity of the Fourier transformation it follows that the linear information is entirely represented by the Fourier amplitudes. Hence, all nonlinear information is contained solely in the Fourier phases. Yet, the direct study of the Fourier phases has so far attracted only little attention. Here, we present a novel method to quantify the phase information. In close analogy to random walk analyses, we propose the phase walk statistics as a way to quantify the phase information. We apply it to the analysis of nonlinearities in intermittent, leptokurtic time series like turbulent wind data, the Dow Jones (DJ) day-to-day returns and synthetic leptokurtic data. Testing for nonlinearities by means of surrogates shows that the new method yields strong significances for nonlinear behavior. Due to the drastically decreased computing time as compared to embedding space methods, the number of surrogate realizations can be increased by orders of magnitude [1]. Thereby, the probability distribution of the test statistics can very accurately be derived and parameterized, which allows for much more precise tests on nonlinearities. [1] K. Schreiber et al., Chaos, 28, 063120 (2018)

Item URL in elib:https://elib.dlr.de/127108/
Document Type:Conference or Workshop Item (Speech)
Title:Phase walk analysis of leptokurtic time series
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Räth, ChristophChristoph.Raeth (at) dlr.deUNSPECIFIED
Modest, HeikeHeike.Modest (at) dlr.deUNSPECIFIED
Schreiber, KorbinianKorbinian.Schreiber (at) dlr.deUNSPECIFIED
Date:April 2019
Refereed publication:No
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Status:Unpublished
Keywords:Nonlinear time series analysis, Fourier transformation, Surrogates, Stock market, Turbulence
Event Title:DPG Frühjahrestagung
Event Location:Regensburg
Event Type:international Conference
Event Dates:1.-5. April 2019
Organizer:DPG
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
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Materials Physics in Space > Research Group Complex Plasma
Deposited By: Räth, Christoph
Deposited On:15 Apr 2019 08:02
Last Modified:15 Apr 2019 08:02

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