Detecting time lag between a pair of time series using visibility graph algorithm.

Area of Science:

• Time series analysis
• Graph theory applications
• Statistical modeling

Background:

• Estimating time lags between paired time series is crucial for many applications.
• Current cross-correlation methods have limitations in accurately detecting these lags.
• The visibility graph algorithm offers a novel approach to time series analysis.

Purpose of the Study:

• To introduce and evaluate a new method for quantifying time lags using the visibility graph algorithm.
• To compare the performance of the new method against traditional cross-correlation techniques.
• To explore the applicability of the new method in neuroscience and environmental epidemiology.

Main Methods:

• Adapting the visibility graph algorithm to convert time series into mathematical graphs.
• Conducting extensive simulation studies to assess method performance under various scenarios.
• Developing a likelihood-based parametric modeling framework for uncertainty quantification and hypothesis testing.

Main Results:

• The visibility graph method accurately and unambiguously identified time lags in simulated data where cross-correlation failed.
• Simulation studies provided insights into scenarios where the new method excels and where it may be outperformed.
• The method was successfully applied to case studies in neuroscience and environmental epidemiology.

Conclusions:

• The visibility graph method presents a robust alternative for time lag estimation in time series analysis.
• This approach offers improved accuracy and clarity compared to conventional cross-correlation methods.
• The method has demonstrated practical utility in diverse scientific fields.