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Codifference can detect ergodicity breaking and non-Gaussianity

  • We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a nonlinear analogue of the mean squared displacement.

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Metadaten
Author:Jakub ŚlęzakORCiD, Ralf MetzlerORCiD, Marcin MagdziarzORCiD
DOI:https://doi.org/10.1088/1367-2630/ab13f3
ISSN:1367-2630
Parent Title (English):New Journal of Physics
Publisher:Deutsche Physikalische Gesellschaft
Place of publication:Bad Honnef
Document Type:Article
Language:English
Date of first Publication:2019/05/06
Year of Completion:2019
Release Date:2019/10/09
Tag:anomalous diffusion; diffusion; stochastic time series
Volume:21
Pagenumber:25
Funder:Universität Potsdam
Grant Number:PA 2019_32
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Peer Review:Referiert
Grantor:Publikationsfonds der Universität Potsdam
Publication Way:Open Access
Licence (German):License LogoCreative Commons - Namensnennung, 3.0 Deutschland
Notes extern:Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 748