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 applicabil...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2019-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ab13f3 |
| _version_ | 1797750160129785856 |
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| author | Jakub Ślęzak Ralf Metzler Marcin Magdziarz |
| author_facet | Jakub Ślęzak Ralf Metzler Marcin Magdziarz |
| author_sort | Jakub Ślęzak |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T16:28:42Z |
| format | Article |
| id | doaj.art-a803bd0d5ec545ca80149c3dd87b028e |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:28:42Z |
| publishDate | 2019-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-a803bd0d5ec545ca80149c3dd87b028e2023-08-08T15:36:26ZengIOP PublishingNew Journal of Physics1367-26302019-01-0121505300810.1088/1367-2630/ab13f3Codifference can detect ergodicity breaking and non-GaussianityJakub Ślęzak0https://orcid.org/0000-0002-0683-2831Ralf Metzler1https://orcid.org/0000-0002-6013-7020Marcin Magdziarz2https://orcid.org/0000-0002-2239-7155Department of Physics, Bar Ilan University , Israel; Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology , PolandInstitute of Physics and Astronomy, Potsdam University , GermanyFaculty of Pure and Applied Mathematics, Wrocław University of Science and Technology , PolandWe 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.https://doi.org/10.1088/1367-2630/ab13f3diffusionanomalous diffusionstochastic time series |
| spellingShingle | Jakub Ślęzak Ralf Metzler Marcin Magdziarz Codifference can detect ergodicity breaking and non-Gaussianity New Journal of Physics diffusion anomalous diffusion stochastic time series |
| title | Codifference can detect ergodicity breaking and non-Gaussianity |
| title_full | Codifference can detect ergodicity breaking and non-Gaussianity |
| title_fullStr | Codifference can detect ergodicity breaking and non-Gaussianity |
| title_full_unstemmed | Codifference can detect ergodicity breaking and non-Gaussianity |
| title_short | Codifference can detect ergodicity breaking and non-Gaussianity |
| title_sort | codifference can detect ergodicity breaking and non gaussianity |
| topic | diffusion anomalous diffusion stochastic time series |
| url | https://doi.org/10.1088/1367-2630/ab13f3 |
| work_keys_str_mv | AT jakubslezak codifferencecandetectergodicitybreakingandnongaussianity AT ralfmetzler codifferencecandetectergodicitybreakingandnongaussianity AT marcinmagdziarz codifferencecandetectergodicitybreakingandnongaussianity |