Kernel-based joint independence tests for multivariate stationary and non-stationary time series

Area of Science:

• Statistics
• Data Science
• Time Series Analysis

Background:

• Multivariate time-series data are common in many fields.
• Understanding inter-variable dependencies is key for accurate analysis.
• Existing methods may not capture complex, higher-order relationships.

Purpose of the Study:

• To introduce novel kernel-based statistical tests for joint independence in multivariate time series.
• To extend the Hilbert-Schmidt independence criterion for stationary and non-stationary processes.
• To provide a robust method for uncovering higher-order interactions in complex data.

Main Methods:

• Kernel-based statistical tests extending the d-variable Hilbert-Schmidt independence criterion.
• Application to both stationary and non-stationary multivariate time series.
• Utilizing resampling techniques for single- and multiple-realization time series.

Main Results:

• Successfully uncovered significant higher-order dependencies in synthetic data (frequency mixing, logic gates).
• Demonstrated robustness in real-world datasets from climate, neuroscience, and socio-economics.
• Validated the method's ability to detect complex interactions.

Conclusions:

• The developed method enhances the analysis of multivariate time series.
• It provides a valuable tool for uncovering high-order interactions in diverse data.
• Broadens the applicability of statistical independence tests to real-world systems.