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Random Error01:04

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Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Estimating Permutation Entropy Variability via Surrogate Time Series.

Leonardo Ricci1,2, Alessio Perinelli1

  • 1Department of Physics, University of Trento, 38123 Trento, Italy.

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|July 27, 2022
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Summary
This summary is machine-generated.

This study introduces a new method to assess the statistical significance of changes in permutation entropy (PE) for time series analysis. The approach uses surrogate time series to reliably estimate PE uncertainty, making randomness analysis more robust.

Keywords:
permutation entropysurrogate generationuncertainty estimation

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Area of Science:

  • Complexity Science
  • Time Series Analysis
  • Statistical Physics

Background:

  • Permutation Entropy (PE) is widely used to quantify randomness in time series.
  • Inferring source dynamics from PE changes is common, but statistical significance is often overlooked.
  • Estimating PE uncertainty from a single time series is challenging.

Purpose of the Study:

  • To develop a method for assessing the statistical significance of changes in permutation entropy.
  • To address the challenge of estimating PE uncertainty from time series data.
  • To provide a reliable and accessible tool for time series randomness analysis.

Main Methods:

  • Generation of surrogate time series to estimate permutation entropy uncertainty.
  • Application of the method to both synthetic and experimental time series data.
  • Utilizing widely available numerical tools for implementation.

Main Results:

  • The proposed method reliably assesses the statistical significance of PE changes.
  • The approach effectively estimates the uncertainty associated with PE values.
  • Demonstrated reliability on diverse datasets.

Conclusions:

  • The developed method enhances the robustness of time series randomness analysis using permutation entropy.
  • It overcomes the limitation of assessing PE uncertainty, enabling more rigorous interpretations.
  • The approach is computationally affordable and readily implementable for researchers.