Identifying Ordinal Similarities at Different Temporal Scales

Area of Science:

• Data Science
• Complex Systems Analysis
• Time Series Analysis

Background:

• Time series data analysis is crucial in many scientific fields.
• Identifying similarities across multiple temporal scales remains a challenge.
• Existing methods may not capture ordinal patterns effectively.

Purpose of the Study:

• To implement and validate the permutation Jensen-Shannon distance for time series analysis.
• To assess the method's capability in discerning ordinal patterns and similarities across temporal scales.
• To demonstrate the practical application of this metric in a complex photonic system.

Main Methods:

• Numerical analysis to validate multiscale capabilities.
• Application of the permutation Jensen-Shannon distance to time series data.
• Comparative analysis of time series patterns at different temporal resolutions.

Main Results:

• The permutation Jensen-Shannon distance effectively identifies ordinal similarities between time series.
• The method's multiscale capabilities were numerically validated.
• Successful application demonstrated in a complex photonic system, highlighting practical utility.

Conclusions:

• The permutation Jensen-Shannon distance is a robust tool for analyzing time series data.
• This metric precisely identifies temporal scales of ordinal similarity.
• The approach holds broad applicability across diverse scientific disciplines for time series analysis.