Return interval distribution of extreme events and long-term memory

Area of Science:

• Complex Systems Analysis
• Statistical Physics
• Time Series Analysis

Background:

• Understanding extreme events and their recurrence is vital across many scientific disciplines.
• Physical systems often exhibit long-range correlations, influencing the timing of extreme events.
• Previous research suggested stretched exponential distributions for return intervals in such systems, based on simulations.

Purpose of the Study:

• To derive an analytical expression for the distribution of return intervals in long-range correlated time series.
• To characterize the behavior of extreme events in systems with long-range correlations.
• To investigate the dependence of return interval distributions on the threshold for defining extreme events.

Main Methods:

• Analytical derivation of return interval distribution for large average return intervals.
• Numerical simulations to validate theoretical findings.
• Analysis of the influence of threshold selection on event recurrence patterns.

Main Results:

• An analytical expression for return interval distribution was obtained.
• The distribution was found to be a product of a power law and a stretched exponential form.
• The study clarifies the validity regimes for this analytical model.

Conclusions:

• The derived analytical model accurately describes return interval distributions in long-range correlated time series.
• This provides a more precise tool for analyzing extreme events in complex systems.
• The findings enhance our understanding of recurrence patterns influenced by long-range correlations and event thresholds.