Title: Causal discovery from conditionally stationary time series. Abstract: Causal discovery, i.e., inferring underlying causal relationships from observational data, has been shown to be highly challenging for AI systems. In time series modeling context, traditional causal discovery methods mainly consider constrained scenarios with fully observed variables and/or data from stationary time-series. We develop a causal discovery approach to handle a wide class of non-stationary time-series that are conditionally stationary, where the non-stationary behaviour is modeled as stationarity conditioned on a set of (possibly hidden) state variables. Named state-dependent causal inference (SDCI), our approach is able to recover the underlying causal dependencies, provably with fully-observed states and empirically with hidden states. The latter is confirmed by experiments on synthetic linear system and nonlinear particle interaction data, where SDCI achieves superior performance over baseline causal discovery methods. Improved results over non-causal RNNs on modeling NBA player movements demonstrate the potential of our method and motivate the use causality-driven methods for forecasting.