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Ordinal Random Processes.

Christoph Bandt1

  • 1Institute of Mathematics, University of Greifswald, 17487 Greifswald, Germany.

Entropy (Basel, Switzerland)
|June 26, 2025
PubMed
Summary

This study introduces theoretical models for ordinal pattern frequencies, demonstrating they can be determined without numerical data. It also defines stationary order for developing statistical methods for ordinal time series.

Area of Science:

  • Time series analysis
  • Statistical modeling

Background:

  • Ordinal patterns are valuable tools across various scientific fields.
  • There is a need for robust theoretical models to analyze ordinal patterns.

Purpose of the Study:

  • To address the need for theoretical models for ordinal pattern analysis.
  • To establish a genuine statistical methodology for ordinal time series.

Main Methods:

  • Developing a model for frequencies of ordinal patterns.
  • Specifying the concept of stationary order.
  • Identifying fundamental problems for statistical methodology.

Main Results:

  • A model for ordinal pattern frequencies can be determined without numerical values.
Keywords:
ordinal patternpermutation entropystochastic processtime series

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  • The concept of stationary order is specified.
  • Key challenges for developing a statistical methodology are outlined.

    • Conclusions:

    • Theoretical models for ordinal patterns can be established without empirical data.
    • Defining stationary order is crucial for advancing ordinal time series analysis.
    • Further research is needed to develop a comprehensive statistical methodology.