Evaluating Methods for Detrending Time Series Using Ordinal Patterns, with an Application to Air Transport Delays

Area of Science:

• Complex Systems Analysis
• Network Science
• Time Series Analysis

Background:

• Functional networks are crucial for understanding complex system connectivity through observed dynamics.
• A key assumption for reliable functional network analysis is the stationarity of time series data.
• Non-stationarity can introduce spurious functional connections, complicating analysis.

Purpose of the Study:

• To introduce and validate ordinal patterns as a method for assessing the effectiveness of detrending techniques.
• To evaluate detrending methods on real-world airport delay data and synthetic datasets.
• To provide operational conclusions on managing time series stationarity in functional network analysis.

Main Methods:

• Utilized ordinal patterns and derived metrics to quantify time series properties.
• Applied detrending methods to time series data.
• Assessed the impact of detrending on functional connectivity using ordinal pattern analysis.

Main Results:

• Demonstrated that ordinal patterns can effectively detect residual non-stationarity after detrending.
• Showcased the application of this method to airport delay data from European and US systems.
• Provided evidence of how non-stationarity and its correction affect the observed functional connections.

Conclusions:

• Ordinal pattern analysis offers a robust tool for validating detrending effectiveness in complex systems.
• Proper detrending is essential to avoid spurious connections in functional network analysis.
• The findings have implications for understanding propagation dynamics in real-world systems like air traffic.