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Nonlinear parametric model for Granger causality of time series
Daniele Marinazzo1, Mario Pellicoro, Sebastiano Stramaglia
1TIRES-Center of Innovative Technologies for Signal Detection and Processing, Università di Bari, Bari, Italy.
Summary
We introduce a new nonlinear Granger causality method using radial basis functions. This approach reveals symmetric causal links in sepsis patients and quantifies neural network influences.
Area of Science:
- Time series analysis
- Nonlinear dynamics
- Causal inference
Background:
- Granger causality assesses predictive relationships between time series.
- Existing methods often assume linear or additive relationships.
- Nonlinear interactions are crucial in many complex systems.
Purpose of the Study:
- To propose a novel nonlinear Granger causality measure.
- To evaluate causality in complex, non-additive systems.
- To demonstrate the method's utility in physiological and neural systems.
Main Methods:
- Utilizing a radial basis function (RBF) approach.
- Developing a flexible model capable of approximating arbitrary functions.
- Applying the RBF model to nonlinear Granger causality assessment.
Main Results:
- Identified symmetric causal relationships between heart rate and blood pressure in sepsis patients, unlike in congestive heart failure.
- Quantified the combined influence of couplings and membrane time constants in a neural network feedback loop.
- Demonstrated the model's ability to capture nonlinear causal influences.
Conclusions:
- The RBF-based nonlinear Granger causality is effective for complex systems.
- This method provides new insights into physiological and neural dynamics.
- It offers a powerful tool for analyzing nonlinear causal interactions.