Inference of couplings between variables of a given system using causal wavelets, causal information, equations...

Area of Science:

• Dynamical Systems and Chaos Theory
• Time Series Analysis
• Causality Inference

Background:

• Inferring directional couplings from observational time series is a complex problem in dynamical systems.
• Existing methods often struggle with real-world data, especially with stochastic perturbations and low correlations.

Purpose of the Study:

• To evaluate the capabilities of various causality inference techniques on deterministic and partially deterministic systems.
• To identify robust methods for detecting direct and indirect causal relationships in complex systems.

Main Methods:

• Simulation of two coupled 3D chaotic subsystems (dissipative and conservative) with varying coupling strengths.
• Application and evaluation of techniques: correlation, mutual information, Granger causality, wavelet coherence, bivariate global modeling, and equation reconstruction.
• Testing on observational groundwater level data from the Se San River basin.

Main Results:

• Most tested techniques showed poor performance in detecting direct couplings and robustness against noise and weak couplings.
• Bivariate global modeling and equation reconstruction techniques demonstrated superior effectiveness in inferring causality.
• Detecting weak bidirectional couplings proved particularly challenging under noisy conditions.

Conclusions:

• Bivariate modeling and equation reconstruction are the most promising approaches for causality inference in complex dynamical systems.
• The study highlights the challenges of inferring causality with real-world, noisy time series data.
• Deterministic, complex couplings were identified in groundwater levels of the Se San River basin.