Sortability of Time Series Data

TL;DR

This paper explores how dataset characteristics like varsortability and R^2-sortability, originally studied in causal discovery, also apply to autocorrelated time series data, revealing insights into causal information contained in scales.

Contribution

It adapts var- and R^2-sortability measures to time series data and empirically investigates their relationship with causal discovery performance across diverse datasets.

Findings

Real-world datasets show high varsortability and low R^2-sortability.

Dataset characteristics influence the effectiveness of causal discovery methods.

Scales may carry significant causal information in time series data.

Abstract

Evaluating the performance of causal discovery algorithms that aim to find causal relationships 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 $R^2$-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 Erd\H{o}s-R\'enyi 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 $R^2$-sortability to time series data. We also investigate the extent to which the performance of 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 varsortability and low $R^2$-sortability indicating that scales may carry a significant amount of causal information.