Dynamical Causal Effects in Bidirectionally Coupled Stochastic Damped Oscillators

Abstract

Diverse causality quantifiers used in time series analysis are promising tools for solving many research and diagnostic problems. The recently proposed framework of dynamical causal effects (DCEs) provides a unifying formalism that allows one to express various causality quantifiers as specific DCEs and relate them to each other. Within the framework of DCEs, this work studies relationships between several well-known quantifiers (transfer entropy, Granger-Geweke causality spectrum, coupling spectral effects) and oscillation-theoretic phenomena (arousal of spectral peaks, amplitude modulation) in the classical system of two stochastic linear damped oscillators. Thereby, a qualitative oscillation-theoretic interpretation of the numerical values of the causality quantifiers is established that promises to make their future applications more efficient.