A continuous ordinal patterns-based paradigm for the analysis and comparison of time series

Area of Science:

• Complex Systems Analysis
• Time Series Analysis
• Machine Learning

Background:

• Traditional time series analysis methods face challenges in capturing complex dynamics.
• Reservoir computing offers a powerful framework for processing sequential data.
• Ordinal patterns provide a robust way to characterize time series behavior.

Purpose of the Study:

• To introduce a novel method for comparing time series by integrating continuous ordinal patterns with reservoir computing.
• To develop a technique capable of assessing properties like stochasticity and time irreversibility.
• To validate the method's effectiveness across synthetic and real-world datasets.

Main Methods:

• Utilizing continuous ordinal patterns as non-linear transformation units within a reservoir computing architecture.
• Transforming time series data using this novel architecture.
• Classifying the transformed time series with a standard machine learning model to compute distances.

Main Results:

• The method successfully calculates distances between time series and reference versions (e.g., shuffled, time-reversed).
• Demonstrated higher sensitivity compared to classical tests in identifying properties of chaotic systems.
• Validated on diverse real-world data from financial, medical, and technological domains.

Conclusions:

• The proposed method offers a sensitive and effective approach for time series comparison and property testing.
• The integration of ordinal patterns and reservoir computing provides a powerful tool for complex system analysis.
• The method shows promise for generalizability and robustness across various applications.