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Universal and non-universal properties of recurrence intervals of rare events

Author

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  • Zhao, Xiaojun
  • Shang, Pengjian
  • Lin, Aijing

Abstract

This paper is devoted to the statistical analysis on the recurrence intervals of rare events that are defined above a given threshold. The memory property of original records is found to have significant effects on the distribution and the correlation structure of recurrence intervals, so that some universal and non-universal properties arise. (i) For long-range persistent records by the ARFIMA processes, where large values are likely to follow large values, the recurrence intervals yield stretched exponential distributions and further show long-range persistence. (ii) For long-range anti-persistent records by the ARFIMA processes, the recurrence intervals obey exponential distributions, also absence of autocorrelation. (iii) For short-range autocorrelated records, the distribution and the correlation structure of recurrence intervals both depend on the parameters of the model and the threshold of rare events.

Suggested Citation

  • Zhao, Xiaojun & Shang, Pengjian & Lin, Aijing, 2016. "Universal and non-universal properties of recurrence intervals of rare events," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 132-143.
    • Handle: RePEc:eee:phsmap:v:448:y:2016:i:c:p:132-143
    DOI: 10.1016/j.physa.2015.12.082
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    Cited by:

    1. Zhao, Xiaojun & Zhang, Pengyuan, 2020. "Multiscale horizontal visibility entropy: Measuring the temporal complexity of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).

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