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Compression complexity with ordinal patterns for robust causal inference in irregularly sampled time series.

Aditi Kathpalia1, Pouya Manshour1, Milan Paluš2

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We introduce Permutation CCC (PCCC), a new method to determine cause and effect in complex, multidimensional systems. PCCC extends previous causality measures to handle more complex data, including paleoclimate records.

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Area of Science:

  • Causality inference
  • Complex systems analysis
  • Time series analysis

Background:

  • Distinguishing cause from effect is a fundamental challenge across scientific disciplines.
  • Existing causality measures like Compression-Complexity Causality (CCC) are limited to one-dimensional time series.
  • The need for causality assessment in multidimensional systems with complex data is growing.

Purpose of the Study:

  • To extend the applicability of Compression-Complexity Causality (CCC) to multidimensional systems.
  • To introduce a novel causality measure, Permutation CCC (PCCC), capable of analyzing complex, high-dimensional data.
  • To demonstrate the robustness and utility of PCCC on simulated and real-world datasets.

Main Methods:

  • Development of an ordinal pattern symbolization scheme to encode multidimensional data into one-dimensional sequences.
  • Application of the CCC framework to these symbolic sequences to create PCCC.
  • Validation of PCCC using numerical simulations and paleoclimate data.

Main Results:

  • PCCC successfully extends causality estimation to multidimensional systems.
  • The method retains the advantages of CCC, including robustness to irregular sampling, missing data, and finite data lengths.
  • PCCC demonstrated effectiveness on complex paleoclimate data with inherent uncertainties.

Conclusions:

  • Permutation CCC (PCCC) offers a powerful new tool for causality inference in multidimensional systems.
  • PCCC is particularly valuable for analyzing complex, real-world data where traditional methods fall short.
  • This approach has significant implications for fields like climate science and beyond.