dorsal/arxiv
View SchemaRecurrence time analysis, long-term correlations, and extreme events
| Authors | Eduardo G. Altmann, Holger Kantz |
|---|---|
| Categories | |
| ArXiv ID | physics/0503056 |
| URL | https://arxiv.org/abs/physics/0503056 |
| DOI | 10.1103/PhysRevE.71.056106 |
| Journal | Phys. Rev. E 71, 056106 (2005). |
Abstract
The recurrence times between extreme events have been the central point of statistical analyses in many different areas of science. Simultaneously, the Poincar\'e recurrence time has been extensively used to characterize nonlinear dynamical systems. We compare the main properties of these statistical methods pointing out their consequences for the recurrence analysis performed in time series. In particular, we analyze the dependence of the mean recurrence time and of the recurrence time statistics on the probability density function, on the interval whereto the recurrences are observed, and on the temporal correlations of time series. In the case of long-term correlations, we verify the validity of the stretched exponential distribution, which is uniquely defined by the exponent $\gamma$, at the same time showing that it is restricted to the class of linear long-term correlated processes. Simple transformations are able to modify the correlations of time series leading to stretched exponentials recurrence time statistics with different $\gamma$, which shows a lack of invariance under the change of observables.
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"abstract": "The recurrence times between extreme events have been the central point of\nstatistical analyses in many different areas of science. Simultaneously, the\nPoincar\\\u0027e recurrence time has been extensively used to characterize nonlinear\ndynamical systems. We compare the main properties of these statistical methods\npointing out their consequences for the recurrence analysis performed in time\nseries. In particular, we analyze the dependence of the mean recurrence time\nand of the recurrence time statistics on the probability density function, on\nthe interval whereto the recurrences are observed, and on the temporal\ncorrelations of time series. In the case of long-term correlations, we verify\nthe validity of the stretched exponential distribution, which is uniquely\ndefined by the exponent $\\gamma$, at the same time showing that it is\nrestricted to the class of linear long-term correlated processes. Simple\ntransformations are able to modify the correlations of time series leading to\nstretched exponentials recurrence time statistics with different $\\gamma$,\nwhich shows a lack of invariance under the change of observables.",
"arxiv_id": "physics/0503056",
"authors": [
"Eduardo G. Altmann",
"Holger Kantz"
],
"categories": [
"physics.data-an",
"nlin.AO",
"physics.comp-ph"
],
"doi": "10.1103/PhysRevE.71.056106",
"journal_ref": "Phys. Rev. E 71, 056106 (2005).",
"title": "Recurrence time analysis, long-term correlations, and extreme events",
"url": "https://arxiv.org/abs/physics/0503056"
},
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