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Analytically solvable autocorrelation function for weakly correlated interevent times.

Hang-Hyun Jo1

  • 1Asia Pacific Center for Theoretical Physics, Pohang 37673, Republic of Korea; Department of Physics, Pohang University of Science and Technology, Pohang 37673, Republic of Korea; and Department of Computer Science, Aalto University, Espoo FI-00076, Finland.

Physical Review. E
|September 11, 2019
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Summary

This study reveals how correlations between interevent times (IETs) influence long-term temporal correlations in event sequences. Stronger IET correlations lead to steeper autocorrelation function decay, especially in power-law distributions.

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Area of Science:

  • Complex Systems
  • Statistical Physics
  • Time Series Analysis

Background:

  • Natural and social phenomena exhibit long-term temporal correlations characterized by algebraically decaying autocorrelation functions.
  • These correlations arise from heterogeneous interevent times (IETs) and correlations between IETs.
  • The impact of IET correlations on autocorrelation functions remains less understood compared to heterogeneous IETs.

Purpose of the Study:

  • To analytically derive the autocorrelation function for arbitrary IET distributions with weakly correlated IETs.
  • To investigate the specific effects of correlations between consecutive IETs on temporal correlations.
  • To provide a framework for understanding long-term temporal correlations induced by IET correlations.

Main Methods:

  • Derivation of an analytical form for the autocorrelation function.
  • Modeling joint probability distributions of consecutive IETs using the Farlie-Gumbel-Morgenstern copula.
  • Numerical simulations using exponential and power-law IET distributions to validate analytical results.

Main Results:

  • An analytical formula for the autocorrelation function was derived for weakly correlated IETs.
  • Numerical simulations confirmed the analytical findings for both exponential and power-law IET distributions.
  • For power-law IETs, stronger correlations between IETs resulted in a steeper decay of the autocorrelation function.

Conclusions:

  • The study provides a rigorous analytical approach to understand temporal correlations induced by IET correlations.
  • Correlations between interevent times play a significant role in shaping long-term temporal dynamics.
  • This work enhances the understanding of complex event sequences in natural and social systems.