Linear-inverse-modeling approach to estimating Liang-Kleeman information flow in a cyclostationary process under memoryless and persistent noise

The Liang-Kleeman (LK) information flow provides a powerful framework for quantifying causality among variables, while linear inverse modeling (LIM) offers an effective empirical approach to studying the dynamical evolution of system states from input data. In this study, we unify these two concepts by proposing the LIM-LK framework-a data-driven method for estimating LK information flow from input data using LIM. Beyond capturing causality among state variables, the proposed framework establishes a direct connection between causality and system dynamics, and also enables the quantification of entropy transfer from the ambient environment to the system through both memoryless and persistent stochastic forcing. The effectiveness of this unified approach is demonstrated through an application to the interaction between the Pacific and Indian Oceans, offering both causal and dynamical insight into ocean variability and its seasonal modulation.