Assessing time series irreversibility through micro-scale trends

Area of Science:

• Complex systems analysis
• Time series analysis
• Statistical mechanics

Background:

• Time irreversibility analysis is crucial for understanding system dynamics.
• Existing irreversibility metrics have limitations regarding data requirements and computational cost.
• Permutation pattern-based tests are common but may not capture all dynamic aspects.

Purpose of the Study:

• To develop a novel time irreversibility metric.
• To incorporate signal amplitude information into time series analysis.
• To demonstrate the complementary nature of the new metric to existing methods.

Main Methods:

• Building upon permutation pattern concepts.
• Integrating signal amplitude and its temporal evolution.
• Validation using synthetic time series.
• Application to real-world datasets.

Main Results:

• The proposed metric provides complementary information to permutation pattern analysis alone.
• Synthetic data confirm the added value of amplitude information.
• The new metric shows applicability to real-world time series.

Conclusions:

• No single irreversibility metric is universally optimal.
• The developed metric offers a valuable addition to the toolkit for time series analysis.
• Diverse analytical approaches are necessary for comprehensive understanding of complex system dynamics.