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.
Author details: | Jakub ŚlęzakORCiD, Ralf MetzlerORCiDGND, Marcin MagdziarzORCiD |
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DOI: | https://doi.org/10.1088/1367-2630/ab13f3 |
ISSN: | 1367-2630 |
Title of parent work (English): | New Journal of Physics |
Publisher: | Deutsche Physikalische Gesellschaft |
Place of publishing: | Bad Honnef |
Publication type: | Article |
Language: | English |
Date of first publication: | 2019/05/06 |
Publication year: | 2019 |
Release date: | 2019/10/09 |
Tag: | anomalous diffusion; diffusion; stochastic time series |
Volume: | 21 |
Number of pages: | 25 |
Funding institution: | Universität Potsdam |
Funding number: | PA 2019_32 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer review: | Referiert |
Grantor: | Publikationsfonds der Universität Potsdam |
Publishing method: | Open Access |
License (German): | Creative Commons - Namensnennung, 3.0 Deutschland |
External remark: | Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 748 |