# Sortability of Time Series Data

arXiv: https://arxiv.org/abs/2407.13313 · HTML: https://mlsanity.com/paper/2407.13313/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 20 references that are in the map.
- First posted on arXiv 18 Jul 2024.

## Builds on (most cited first, 10 of 10)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets](https://mlsanity.com/paper/2003.03685/) (2020)
- [Structure Learning with Continuous Optimization: A Sober Look and Beyond](https://mlsanity.com/paper/2304.02146/) (2023)
- [Neural Additive Vector Autoregression Models for Causal Discovery in Time Series](https://mlsanity.com/paper/2010.09429/) (2020)
- [A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Models](https://mlsanity.com/paper/2303.18211/) (2023)
- [Causal structure learning from time series: Large regression coefficients may predict causal links better in practice than small p-values](https://mlsanity.com/paper/2002.09573/) (2020)
- [The Causal Chambers: Real Physical Systems as a Testbed for AI Methodology](https://mlsanity.com/paper/2404.11341/) (2024)
- [Estimating a Directed Tree for Extremes](https://mlsanity.com/paper/2102.06197/) (2021)

## Built on by (most cited first, 3 of 3)

- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [Unitless Unrestricted Markov-Consistent SCM Generation: Better Benchmark Datasets for Causal Discovery](https://mlsanity.com/paper/2503.17037/) (2025)
- [Causal Discovery for Irregularly Time Series with Consistency Guarantees](https://mlsanity.com/paper/2507.03310/) (2025)

## Abstract (arXiv)

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 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 ErdHos-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 R2-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 R2-sortability indicating that scales may carry a significant amount of causal information.