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

• 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.