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Extreme value statistics in records with long-term persistence.

Jan F Eichner1, Jan W Kantelhardt, Armin Bunde

  • 1Institut für Theoretische Physik III, Justus-Liebig-Universität Giessen, 35392 Giessen, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
PubMed
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Long-term correlations in natural data influence extreme event statistics. The study reveals that previous extreme events significantly impact future maxima, suggesting conditional analysis for better prediction.

Area of Science:

  • Complex Systems
  • Time Series Analysis
  • Statistical Physics

Background:

  • Natural records often display long-term correlations, characterized by power-law decay in autocorrelation functions (C(s) ~ s-gamma).
  • Understanding the statistical properties of extreme events in such correlated data is crucial for risk assessment and prediction.

Purpose of the Study:

  • To investigate the impact of long-term correlations on the statistical behavior of extreme events (maxima) in time series.
  • To determine if the distribution and magnitude of extreme events are influenced by the history of the data, particularly previous maxima.

Main Methods:

  • Numerical simulations were employed to study time series with power-law correlations.
  • Analysis focused on the integrated distribution function of maxima within fixed duration segments (R).

Related Experiment Videos

  • Investigated the dependence of maxima statistics on initial data distribution and correlation properties.

    • Main Results:

    • The distribution of maxima converges to a Gumbel distribution for large segment durations (R), similar to uncorrelated data.
    • Deviations from Gumbel distribution for finite R depend on initial data properties and correlation strength.
    • Maxima series exhibit long-term correlations mirroring the original data.
    • Crucially, maxima distribution and mean maxima are significantly dependent on historical data, especially the preceding maximum.

    Conclusions:

    • The dependence of extreme event statistics on preceding events necessitates the use of conditional probability distributions for improved prediction.
    • Conditional mean maxima and conditional maxima distributions, considering the value of the previous maximum, are recommended for enhanced extreme event forecasting.
    • This history dependence is observed in both simulated and actual long-term correlated observational records.