Statistics of Extreme Values in Time Series with Intermediate-Term Correlations

TL;DR

This paper investigates the statistics of extreme values in time series with intermediate-term correlations, revealing that return intervals follow a stretched exponential distribution, challenging the notion that this is exclusive to long-term correlations.

Contribution

It demonstrates through numerical analysis that non-exponential, non-power-law decay correlations produce stretched exponential return interval distributions, expanding understanding of extreme value statistics.

Findings

Return intervals follow a stretched exponential distribution.

Distribution largely independent of threshold.

Challenged the idea that stretched exponential is exclusive to long-term correlations.

Abstract

It will be discussed the statistics of the extreme values in time series characterized by finite-term correlations with non-exponential decay. Precisely, it will be considered the results of numerical analyses concerning the return intervals of extreme values of the fluctuations of resistance and defect-fraction displayed by a resistor with granular structure in a nonequilibrium stationary state. The resistance and defect-fraction are calculated as a function of time by Monte Carlo simulations using a resistor network approach. It will be shown that when the auto-correlation function of the fluctuations displays a non-exponential and non-power-law decay, the distribution of the return intervals of extreme values is a stretched exponential, with exponent largely independent of the threshold. Recently, a stretched exponential distribution of the return intervals of extreme values has been identified in long-term correlated time series by Bunde et al. (2003) and Altmann and Kantz (2005). Thus, the present results show that the stretched exponential distribution of the return intervals is not an exclusive feature of long-term correlated time series.