Article ID Journal Published Year Pages File Type
974493 Physica A: Statistical Mechanics and its Applications 2016 12 Pages PDF
Abstract

•Recurrence intervals of long-range persistent records obey stretched exponential.•Recurrence intervals of long-range anti-persistent records obey exponential.•Recurrence intervals of long-range anti-persistent records are uncorrelated.•Non-universal properties of recurrence intervals of short-range autocorrelated records exist.

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.

Related Topics
Physical Sciences and Engineering Mathematics Mathematical Physics
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