Bandt-Pompe symbolization dynamics for time series with tied values: A data-driven approach

Area of Science:

• Complexity Science
• Nonlinear Dynamics
• Time Series Analysis

Background:

• The Bandt and Pompe method (2002) uses symbolic encoding for permutation entropy.
• Time series with tied (equal) values pose challenges for standard analysis.
• Previous work highlighted potential for false conclusions with tied values.

Purpose of the Study:

• To review existing methods for handling tied values in time series.
• To introduce a novel data-driven imputation technique.
• To improve the accuracy of permutation entropy calculations.

Main Methods:

• Review and classification of existing methodologies for tied value treatment.
• Development and application of a novel data-driven imputation strategy.
• Comparative analysis of the proposed method against existing techniques.

Main Results:

• Existing methods for tied values have limitations.
• The novel imputation method effectively handles tied values.
• The proposed approach avoids false conclusions regarding temporal structures.

Conclusions:

• Accurate treatment of tied values is crucial for reliable time series analysis.
• The new data-driven imputation method offers superior performance.
• This work enhances the robustness of permutation entropy applications.