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| Titel |
On the surprising robustness of the surplus run length and size ratio formulae, and their application to bursts in natural time series |
| VerfasserIn |
Nick Watkins, Sandra Chapman, Philip Hush |
| Konferenz |
EGU General Assembly 2014
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 16 (2014) |
| Datensatznummer |
250093055
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| Publikation (Nr.) |
 EGU/EGU2014-7425.pdf |
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| Zusammenfassung |
| Bursts, events that begin when a time series exceeds a threshold, and end when it drops below
it, have been widely studied in models of intermittent dynamical systems such as SOC and
turbulence, and in natural datasets. Analytical approaches to bursts are needed which permit
handling time dependence and heavy tailed amplitudes, and make contact with mature
mathematics such as the theory of random fields and level crossings. We will discuss one
such technique, which we call the surplus run length ratio [SRLR] formula, which states that
the expectation value of the time between successive up and down- crossings of a
threshold by values of stationary time series from a stochastic process is the empirical
survival function of the process divided by the time rate of upcrossings at that level
[Volkonskii, 1960; Cramer and Leadbetter,1967. We show that the SRLR formula, and
a similar formula relating the integrated burst to the SRLR and the mean excess
function, apply surprisingly widely in highly skewed (lognormal), heavy tailed
(alpha-stable) and long range dependent (fractional Gaussian) cases, among others. We
demonstrate its utility on a non- Gaussian, correlated, natural example which has
been previously studied using bursts, the auroral electrojet (AE) ionospheric index. |
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