Recording the evolution of complex systems over time often yields time series data, which are sequences of observations ordered by time. When multiple variables of a system interact, false correlations may arise. This can lead to erroneous conclusions about the study at hand. Thus, a deeper understanding of the underlying mechanisms requires estimating how changes to one component propagate through the system. However, when the data are purely observational, no experiments or intervention can be performed. Therefore, causal discovery can be employed to infer which variables causally influence each other from data, aiming to learn the underlying causal structure (often a causal graph). This presentation focuses on constraint-based methods for causal discovery in time series data, a family of methods relying on statistical independence tests to build a causal representation of the data. Yet, those tests do not always offer theoretical guarantees on Type I and Type Il error control, especially when the data are not independent and identically distributed (iid). This can largely affect the performance of causal discovery algorithms. Furthermore, such tests can be computationally expensive, which becomes a real problem in constraint-based algorithms where they are repeated many times. To address this issue, we present non-parametric independence tests for time series that offer theoretical guarantees, while significantly reducing algorithmic complexity. By coupling them with regression methods, we propose a complete causal discovery method for time series data.
