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Related Experiment Video

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Inferring long memory using extreme events.

Dayal Singh Kalra1, M S Santhanam1

  • 1Indian Institute of Science Education and Research, Dr. Homi Bhabha Road, Pune 411008, India.

Chaos (Woodbury, N.Y.)
|December 9, 2021
PubMed
Summary

Extreme events in time series data can reveal long memory properties, even with noise or missing data. This study shows extreme events alone can accurately infer correlation exponents in complex systems.

Area of Science:

  • Complex systems analysis
  • Time series analysis
  • Statistical physics

Background:

  • Natural and physical processes often exhibit long memory and extreme events.
  • Time series data in these systems are frequently corrupted by noise and missing values.
  • Extreme events are less affected by noise and missing data compared to typical values.

Purpose of the Study:

  • To investigate if extreme events in a time series can be used to infer its correlation properties.
  • To develop a method for estimating long memory exponents from extreme events.
  • To validate the approach using empirical time series data.

Main Methods:

  • Construction of modified time series using only extreme events.
  • Application of detrended fluctuation analysis (DFA) to original and modified time series.

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  • Comparison of correlation exponents derived from original and extreme-event-based time series.

    • Main Results:

    • A relationship was established between the correlations of the original time series and the modified time series derived from extreme events.
    • The detrended fluctuation analysis exponent, a measure of correlation, was consistently inferred from extreme events.
    • The method proved effective across several real-world empirical time series.

    Conclusions:

    • Correlation properties, specifically long memory exponents, of a time series can be reliably inferred using only its extreme events.
    • This approach offers a robust method for analyzing time series data contaminated with noise or missing values.
    • The findings have implications for understanding and modeling complex systems exhibiting long-range dependence.