Detecting Nonlinear Interactions in Complex Systems: Application in Financial Markets

Area of Science:

• Complex systems analysis
• Nonlinear dynamics
• Time series analysis

Background:

• Structural breaks in complex systems can indicate underlying mechanism changes.
• Standard change-point detection methods may miss nonlinear interactions.
• Detecting nonlinear causality is crucial for understanding system dynamics.

Purpose of the Study:

• To develop a novel scheme for detecting structural breaks by identifying the emergence or disappearance of nonlinear causal relationships.
• To create a significance resampling test sensitive to nonlinear causality.
• To apply the method to financial data and validate its effectiveness.

Main Methods:

• Developed a significance resampling test for the null hypothesis of no nonlinear causal relationships.
• Utilized a Gaussian instantaneous transform and vector autoregressive (VAR) process for resampling.
• Employed the partial mutual information from mixed embedding (PMIME) measure to estimate Granger causality.
• Applied network characteristics derived from PMIME as test statistics in sliding windows.

Main Results:

• The proposed methodology successfully detected nonlinear causality in synthetic and stochastic systems.
• The scheme accurately identified structural breaks in financial time series during major global events.
• Demonstrated sensitivity to changes in nonlinear interactions signaling shifts in system dynamics.

Conclusions:

• The novel scheme effectively detects structural breaks by monitoring nonlinear causal relationships.
• This method offers improved sensitivity for complex systems compared to standard change-point detection.
• The approach has practical applications in finance, climate science, and other fields analyzing complex systems.