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Phase correlations in leptokurtic time series

Räth, Christoph and Laut, Ingo and Schreiber, Korbinian (2015) Phase correlations in leptokurtic time series. Dynamics Days Europe 2015, 6.-10. Sep. 2015, Exeter, England. (Unpublished)

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Abstract

Many time series of nonlinear origin, like turbulence or financial markets not only exhibit lep- tokurtic (also called heavy-tailed or fat-tailed) probability distribution functions (PDF) but are also classified or characterized by them. In the Fourier representation of these time series these non- linearities must be contained in the phase information. Here, we demonstrate how to exploit this information to both synthesize and analyze leptokurtic time series. We first show that empirical data of market indices show linear phase correlations. Based on these findings we impose a set of linear phase correlations on white Gaussian noise and demonstrate that the so-obtained time series can reproduce the scaling properties of the PDF and volatility remark- ably well [1]. Next we introduce a novel nonlinear statistic called phase walk statistics (PWS), which measures – in close analogy to random walk analyses – the deviation from randomness of the phases. Applying this statistics to a number of empirical and synthetic leptokurtic time series reveals that nonlinear- ities can be detected unprecedented significance. A surrogate-assisted analysis further shows that PWS is able to disentangle different classes of nonlinearities, which have indistinguishable PDFs [2]. In summary, the study of Fourier phases offers new and refined insights into nonlinearities in time series. Thus, this approach opens new ways for better understanding and modelling the underlying nonlinear processes.

Item URL in elib:https://elib.dlr.de/98232/
Document Type:Conference or Workshop Item (Speech)
Title:Phase correlations in leptokurtic time series
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Räth, ChristophDLR Research Group Complex Plasma, OberpfaffenhofenUNSPECIFIED
Laut, IngoDLR Research Group Complex Plasma, OberpfaffenhofenUNSPECIFIED
Schreiber, KorbinianDLR Research Group Complex Plasma, OberpfaffenhofenUNSPECIFIED
Date:9 September 2015
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:No
Status:Unpublished
Keywords:Time series analysis, turbulence, nonlinearity, Fourier transformation, Fourier phases
Event Title:Dynamics Days Europe 2015
Event Location:Exeter, England
Event Type:international Conference
Event Dates:6.-10. Sep. 2015
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:Research Group Complex Plasma
Deposited By: Laut, Ingo
Deposited On:02 Oct 2015 11:15
Last Modified:02 Oct 2015 11:15

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