The effect of long-term correlations on the return periods of rare events

Armin Bunde, Jan F. Eichner, Shlomo Havlin, Jan W. Kantelhardt

Research output: Contribution to journalConference articlepeer-review

90 Scopus citations

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 , 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 languageEnglish
Pages (from-to)1-7
Number of pages7
JournalPhysica A: Statistical Mechanics and its Applications
Volume330
Issue number1-2
DOIs
StatePublished - 1 Dec 2003
EventRandomes and Complexity - Eilat, Israel
Duration: 5 Jan 20039 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.

FundersFunder number
Bundesministerium für Bildung und Forschung
Israel Science Foundation

    Keywords

    • Fluctuation analysis
    • Long-term correlations
    • Rare events
    • Return periods
    • Time series

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