  Causal discovery in time series is a rapidly evolving field with a wide
variety of applications in other areas such as climate science and
neuroscience. Traditional approaches assume a stationary causal graph, which
can be adapted to nonstationary time series with time-dependent effects or
heterogeneous noise. In this work we address nonstationarity via
regime-dependent causal structures. We first establish identifiability for
high-order Markov Switching Models, which provide the foundations for
identifiable regime-dependent causal discovery. Our empirical studies
demonstrate the scalability of our proposed approach for high-order
regime-dependent structure estimation, and we illustrate its applicability on
brain activity data.
