Abstract
The basic assumption of common extreme value statistics is that different events in a time record are uncorrelated. In this case, the return intervals rq of events above a given threshold size q are uncorrelated and follow the Poisson distribution. In recent years there is growing evidence that several hydro-meteorological and physiological records of interest (e.g. river flows, temperatures, heartbeat intervals) exhibit long-term correlations where the autocorrelation function decays as Cx(s) ∼ s -γ, with γ between 0 and 1. Here we study how the presence of long-term correlations changes the statistics of the return intervals rq. We find that (a) the mean return intervals R q=〈rq〉 are independent of γ, (b) the distribution of the rq follows a stretched exponential, lnP q(r) ∼ -(r/Rq)γ, and (c) the return intervals are long-term correlated with an exponent γ′ close to γ.
Original language | English |
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Pages (from-to) | 1-7 |
Number of pages | 7 |
Journal | Physica A: Statistical Mechanics and its Applications |
Volume | 330 |
Issue number | 1-2 |
DOIs | |
State | Published - 1 Dec 2003 |
Event | Randomes and Complexity - Eilat, Israel Duration: 5 Jan 2003 → 9 Jan 2003 |
Bibliographical note
Funding Information:This work has been supported by the Bundesministerium für Bildung und Forschung and the Israel Science Foundation.
Funding
This work has been supported by the Bundesministerium für Bildung und Forschung and the Israel Science Foundation.
Funders | Funder number |
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Bundesministerium für Bildung und Forschung | |
Israel Science Foundation |
Keywords
- Fluctuation analysis
- Long-term correlations
- Rare events
- Return periods
- Time series