Sortability of Time Series Data

Evaluating the performance of causal discovery algorithms that aim to find causal relation-ships between time-dependent processes remains a challenging topic. In this paper, we show that certain characteristics of datasets, such as varsortability Reisach et al. (2021) and R²-sortability Reisach et al. (2023), also occur in datasets for autocorrelated stationary time series. We illustrate this empirically using four types of data: simulated data based on SVAR models and Erdős-Rényi graphs, the data used in the 2019 causality-for-climate challenge (Runge et al., 2019), real-world river stream datasets, and real-world data generated by the Causal Chamber of Gamella et al. (2024). To do this, we adapt var-and R²-sortability to time series data. We also investigate the extent to which the performance of continuous score-based causal discovery methods goes hand in hand with high sortability. Arguably, our most surprising finding is that the investigated real-world datasets exhibit high var-sortability and low R²-sortability indicating that scales may carry a significant amount of causal information.