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Return intervals of rare events in records with long-term persistence

Author

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

Abstract

Many natural records exhibit long-term correlations characterized by a power-law decay of the auto-correlation function, C(s)∼s−γ, with time lag s and correlation exponent 0<γ<1. We study, how the presence of such correlations affects the statistics of the return intervals rq for events above a certain threshold value q. We find that (a) the mean return interval Rq does not depend on γ, (b) the distribution of rq follows a stretched exponential, lnPq(r)∼−(r/Rq)γ, and (c) the return intervals are also long-term correlated with the exponent γ, yielding clustering of both small and large return intervals. We provide indications that both the stretched exponential behaviour and the clustering of rare events can be seen in long temperature records.

Suggested Citation

  • Bunde, Armin & F. Eichner, Jan & Havlin, Shlomo & W. Kantelhardt, Jan, 2004. "Return intervals of rare events in records with long-term persistence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 308-314.
    • Handle: RePEc:eee:phsmap:v:342:y:2004:i:1:p:308-314
    DOI: 10.1016/j.physa.2004.01.069
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    Citations

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    Cited by:

    1. Ren, Fei & Gu, Gao-Feng & Zhou, Wei-Xing, 2009. "Scaling and memory in the return intervals of realized volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(22), pages 4787-4796.
    2. Ren, Fei & Guo, Liang & Zhou, Wei-Xing, 2009. "Statistical properties of volatility return intervals of Chinese stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 881-890.
    3. Zhi-Qiang Jiang & Askery Canabarro & Boris Podobnik & H. Eugene Stanley & Wei-Xing Zhou, 2016. "Early warning of large volatilities based on recurrence interval analysis in Chinese stock markets," Quantitative Finance, Taylor & Francis Journals, vol. 16(11), pages 1713-1724, November.
    4. Xie, Wen-Jie & Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2014. "Extreme value statistics and recurrence intervals of NYMEX energy futures volatility," Economic Modelling, Elsevier, vol. 36(C), pages 8-17.
    5. Chi Zhang & Zhengning Pu & Jiasha Fu, 2018. "The Recurrence Interval Difference of Power Load in Heavy/Light Industries of China," Energies, MDPI, vol. 11(1), pages 1-20, January.
    6. Suo, Yuan-Yuan & Wang, Dong-Hua & Li, Sai-Ping, 2015. "Risk estimation of CSI 300 index spot and futures in China from a new perspective," Economic Modelling, Elsevier, vol. 49(C), pages 344-353.
    7. Batac, Rene & Longjas, Anthony & Monterola, Christopher, 2012. "Statistical distributions of avalanche size and waiting times in an inter-sandpile cascade model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 616-624.

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