Long-range correlation and group-occurrence of return intervals of extreme events

This paper studies the long range correlation of the return intervals of extreme events using the method of percent threshold. In view of return intervals of the extreme events, the long range-correlations of return intervals are studied by simulated time series when the extreme events happened. It is found that the constructed extreme event time series also have the characteristics of long-range correlation if the original time series have one. Meanwhile, the scaling exponents of the two time series are very close, it is very different from the return intervals of stochastic series. The probability density function of time series with long-range correlation has significant difference from the stochastic time series. It was found that there is a group-occurrence phenomenon in the return time series with long-range correlation, so a so-called group occurrence index is defined and computed, the stability of the index is also studied. The results show that the reason of the group occurrence of extreme events series is attributed to the long-range correlation of time series.