Explicit Granger causality in kernel Hilbert spaces.

Area of Science:

• Time Series Analysis
• Causal Inference
• Dynamical Systems

Background:

• Granger causality (GC) is a standard method for inferring cause-effect from time series.
• Existing nonlinear kernel methods offer alternatives but can be further generalized.
• Understanding complex system dynamics requires robust causal inference techniques.

Purpose of the Study:

• To generalize kernel Granger causality by incorporating cross-relations in Hilbert spaces.
• To provide a unified framework that encompasses linear and kernel GC.
• To establish tighter performance bounds using Rademacher complexity.

Main Methods:

• Developed a novel framework for generalized kernel Granger causality.
• Utilized Hilbert spaces to explicitly model cross-relations between variables.
• Applied Rademacher complexity for performance analysis and bounding.

Main Results:

• The proposed method generalizes existing linear and kernel Granger causality techniques.
• Demonstrated improved performance bounds compared to previous methods.
• Successfully applied to identify causality in Rössler systems and El Niño-Southern Oscillation impacts on soil moisture.

Conclusions:

• The generalized kernel Granger causality offers a powerful tool for complex time series analysis.
• This framework advances causal inference in dynamical systems and climate science.
• The method provides a more comprehensive approach to uncovering hidden causal relationships.