Causal Discovery for time series from multiple datasets with latent contexts

Causal discovery from time series data is a typical problem setting across the sciences. Often, multiple datasets of the same system variables are available, for instance, time series of river runoff from different catchments. The local catchment systems then share certain causal parents, such as time-dependent large-scale weather over all catchments, but differ in other catchment-specific drivers, such as the altitude of the catchment. These drivers can be called temporal and spatial contexts, respectively, and are often partially unobserved. Pooling the datasets and considering the joint causal graph among system, context, and certain auxiliary variables enables us to overcome such latent confounding of system variables. In this work, we present a non-parametric time series causal discovery method, J(oint)-PCMCI+, that efficiently learns such joint causal time series graphs when both observed and latent contexts are present, including time lags. We present asymptotic consistency results and numerical experiments demonstrating the utility and limitations of the method.