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Phase walk analysis of leptokurtic time series

Schreiber, Korbinian and Modest, Heike I. and Räth, Christoph (2018) Phase walk analysis of leptokurtic time series. Chaos, 28 (6), 063120. American Institute of Physics (AIP). doi: 10.1063/1.5018301. ISSN 1054-1500.

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Official URL: https://doi.org/10.1063/1.5018301


The Fourier phase information play a key role for the quantified description of nonlinear data. We present a novel tool for time series analysis that identifies nonlinearities by sensitively detecting correlations among the Fourier phases. The method, being called phase walk analysis, is based on well established measures from random walk analysis, which are now applied to the unwrapped Fourier phases of time series. We provide an analytical description of its functionality and demonstrate its capabilities on systematically controlled leptokurtic noise. Hereby, we investigate the properties of leptokurtic time series and their influence on the Fourier phases of time series. The phase walk analysis is applied to measured and simulated intermittent time series, whose probability density distribution is approximated by power laws. We use the day-to-day returns of the Dow-Jones industrial average, a synthetic time series with tailored nonlinearities mimicing the power law behavior of the Dow-Jones and the acceleration of the wind at an Atlantic offshore site. 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. Thereby, the probability distribution of the test statistics can very accurately be derived and parameterized, which allows for much more precise tests on nonlinearities.

Item URL in elib:https://elib.dlr.de/120693/
Document Type:Article
Title:Phase walk analysis of leptokurtic time series
AuthorsInstitution or Email of AuthorsAuthor's ORCID iDORCID Put Code
Date:June 2018
Journal or Publication Title:Chaos
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In ISI Web of Science:Yes
Page Range:063120
Publisher:American Institute of Physics (AIP)
Keywords:time series analysis, Fourier transformation, turbulence, econophysics
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 - Research under Space Conditions
DLR - Research theme (Project):R - Komplexe Plasmen / Data analysis (old)
Location: Oberpfaffenhofen
Institutes and Institutions:Institute of Materials Physics in Space > Research Group Complex Plasma
Deposited By: Räth, Christoph
Deposited On:02 Jul 2018 07:05
Last Modified:13 Jun 2023 14:36

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