# SpaceTime: Causal Discovery from Non-Stationary Time Series

arXiv: https://arxiv.org/abs/2501.10235 · HTML: https://mlsanity.com/paper/2501.10235/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 30 references that are in the map.
- First posted on arXiv 17 Jan 2025.

## Builds on (most cited first, 7 of 7)

- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets](https://mlsanity.com/paper/2003.03685/) (2020)
- [Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesis](https://mlsanity.com/paper/2206.02013/) (2022)
- [Reconstructing regime-dependent causal relationships from observational time series](https://mlsanity.com/paper/2007.00267/) (2020)
- [Causal discovery for time series from multiple datasets with latent contexts](https://mlsanity.com/paper/2306.12896/) (2023)
- [Characterization of causal ancestral graphs for time series with latent confounders](https://mlsanity.com/paper/2112.08417/) (2021)

## Built on by (most cited first, 6 of 6)

- [Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noises](https://mlsanity.com/paper/2506.17065/) (2025)
- [Identifiable Markov Switching Models with Instantaneous Effects and Exponential Families](https://mlsanity.com/paper/2606.02231/) (2026)
- [TTCD:Transformer Integrated Temporal Causal Discovery from Non-Stationary Time Series Data](https://mlsanity.com/paper/2605.08111/) (2026)
- [Modeling Covariate Transition for Efficient Estimation of Longitudinal Treatment Effects in Randomized Experiments](https://mlsanity.com/paper/2605.31443/) (2026)
- [Symmetries and Causality: Causal Effect Identification Beyond IID Data](https://mlsanity.com/paper/2609.03697/) (2026)
- [Beyond Stationarity in Time Series: Discovering Causal Structures and Latent Regimes via Markov Blankets](https://mlsanity.com/paper/2609.05150/) (2026)

## Abstract (arXiv)

Understanding causality is challenging and often complicated by changing causal relationships over time and across environments. Climate patterns, for example, shift over time with recurring seasonal trends, while also depending on geographical characteristics such as ecosystem variability. Existing methods for discovering causal graphs from time series either assume stationarity, do not permit both temporal and spatial distribution changes, or are unaware of locations with the same causal relationships. In this work, we therefore unify the three tasks of causal graph discovery in the non-stationary multi-context setting, of reconstructing temporal regimes, and of partitioning datasets and time intervals into those where invariant causal relationships hold. To construct a consistent score that forms the basis of our method, we employ the Minimum Description Length principle. Our resulting algorithm SPACETIME simultaneously accounts for heterogeneity across space and non-stationarity over time. Given multiple time series, it discovers regime changepoints and a temporal causal graph using non-parametric functional modeling and kernelized discrepancy testing. We also show that our method provides insights into real-world phenomena such as river-runoff measured at different catchments and biosphere-atmosphere interactions across ecosystems.