  Time series data from real-world systems often display non-stationary
behavior, indicating varying statistical characteristics over time. This
inherent variability poses significant challenges in deciphering the underlying
structural relationships within the data, particularly in correlation and
causality analyses, model stability, etc. Recognizing distinct segments or
regimes within multivariate time series data, characterized by relatively
stable behavior and consistent statistical properties over extended periods,
becomes crucial. In this study, we apply the regime identification (RegID)
technique to multivariate time series, fundamentally designed to unveil locally
stationary segments within data. The distinguishing features between regimes
are identified using covariance matrices in a Riemannian space. We aim to
highlight how regime identification contributes to improving the discovery of
causal structures from multivariate non-stationary time series data. Our
experiments, encompassing both synthetic and real-world datasets, highlight the
effectiveness of regime-wise time series causal analysis. We validate our
approach by first demonstrating improved causal structure discovery using
synthetic data where the ground truth causal relationships are known.
Subsequently, we apply this methodology to climate-ecosystem dataset,
showcasing its applicability in real-world scenarios.
