Detecting long-lived autodependency changes in a multivariate system via change point detection and regime switching...

Area of Science:

• Dynamical Systems Analysis
• Statistical Modeling
• Computational Psychiatry

Background:

• Long-lived changes in dynamic system variable autodependency characterize critical events.
• Predicting phenomena like epileptic seizures, volcanic eruptions, and psychiatric conditions requires methods to detect these changes in multivariate time series.
• Current methods may not effectively pinpoint specific parameter changes or handle long-lived shifts.

Purpose of the Study:

• To introduce and compare two novel methods for detecting changes in the autodependency of dynamic system variables.
• To evaluate the performance of these methods in identifying critical events.
• To apply these methods to psychopathology data to investigate emotional inertia before depressive relapse.

Main Methods:

• Kernel Change Point-Autoregression (KCP-AR): An adaptation of Kernel Change Point (KCP) applied to running autocorrelations to focus on parameter changes.
• Regime Switching Autoregressive (AR(1)) Models: Models fitted where only autodependency parameters differ across regimes.
• Simulation Study: Comparison of KCP-AR and regime switching AR(1) under varying conditions of variable correlation.

Main Results:

• KCP-AR outperforms regime switching AR(1) when system variables are uncorrelated.
• Regime switching AR(1) is more reliable when multicollinearity is severe.
• Regime switching AR(1) may produce recurrent switches even for long-lived changes, potentially limiting its applicability.

Conclusions:

• Both KCP-AR and regime switching AR(1) offer valuable approaches for detecting critical changes in dynamic systems.
• The choice of method depends on the specific characteristics of the data, particularly the degree of variable correlation.
• These methods hold promise for understanding and predicting critical events, including psychiatric relapses, by analyzing changes in emotional inertia.