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Coupled dynamical systems are frequently observed in nature, but often notwell understood in terms of their causal structure without additional domainknowledge about the system. Especially when analyzing observational time seriesdata of dynamical systems where it is not possible to conduct controlledexperiments, for example time series of climate variables, it can bechallenging to determine how features causally influence each other. There aremany techniques available to recover causal relationships from data, such asGranger causality, convergent cross mapping, and causal graph structurelearning approaches such as PCMCI. Path signatures and their associated signedareas provide a new way to approach the analysis of causally linked dynamicalsystems, particularly in informing a model-free, data-driven approach toalgorithmic causal discovery. With this paper, we explore the use of pathsignatures in causal discovery and propose the application of confidencesequences to analyze the significance of the magnitude of the signed areabetween two variables. These confidence sequence regions converge with greatersampling length, and in conjunction with analyzing pairwise signed areas acrosstime-shifted versions of the time series, can help identify the presence oflag/lead causal relationships. This approach provides a new way to define theconfidence of a causal link existing between two time series, and ultimatelymay provide a framework for hypothesis testing to define whether one timeseries causes another

Path Signature Area-Based Causal Discovery in Coupled Time Series