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| Titel |
How does the quality of a prediction depend on the magnitude of the events under study? |
| VerfasserIn |
S. Hallerberg, H. Kantz |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 15, no. 2 ; Nr. 15, no. 2 (2008-04-16), S.321-331 |
| Datensatznummer |
250012619
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| Publikation (Nr.) |
 copernicus.org/npg-15-321-2008.pdf |
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| Zusammenfassung |
| We investigate the predictability of extreme events in time series.
The focus of this work is to understand, under which circumstances large events
are better predictable than smaller events. Therefore we use a simple prediction algorithm based on precursory structures
which are identified via the maximum likelihood principle.
Using theses precursory structures we predict threshold crossings in
autocorrelated processes of order one, which are either Gaussian,
exponentially or Pareto distributed. The receiver operating characteristic curve is used as a measure for the quality
of predictions we find that the dependence on the event magnitude is closely linked
to the probability distribution function of the underlying stochastic
process. We evaluate this dependence on the probability distribution function
numerically and in the Gaussian case also analytically. Furthermore, we study predictions of threshold crossings in
correlated data, i.e., velocity increments of a free jet flow. The velocity
increments in the free jet flow are in dependence on the time scale
either asymptotically Gaussian or asymptotically exponential distributed.
If we assume that the optimal precursory structures are used to make the
predictions, we find that large threshold crossings are for all different
types of distributions better predictable. These results are in contrast to
previous results, obtained for the prediction of large increments, which showed
a strong dependence on the probability distribution function of the underlying process. |
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