# Causal Discovery in Semi-Stationary Time Series

arXiv: https://arxiv.org/abs/2407.07291 · HTML: https://mlsanity.com/paper/2407.07291/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 39 references that are in the map.
- First posted on arXiv 10 Jul 2024.

## Builds on (most cited first, 8 of 8)

- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [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)
- [High-recall causal discovery for autocorrelated time series with latent confounders](https://mlsanity.com/paper/2007.01884/) (2020)
- [A fast PC algorithm for high dimensional causal discovery with multi-core PCs](https://mlsanity.com/paper/1502.02454/) (2015)
- [Causal Discovery and Forecasting in Nonstationary Environments with State-Space Models](https://mlsanity.com/paper/1905.10857/) (2019)
- [Enhancing Causal Discovery from Robot Sensor Data in Dynamic Scenarios](https://mlsanity.com/paper/2302.10135/) (2023)
- [Causal Discovery of Dynamic Models for Predicting Human Spatial Interactions](https://mlsanity.com/paper/2210.16535/) (2022)

## Built on by (most cited first, 7 of 7)

- [CAnDOIT: Causal Discovery with Observational and Interventional Data from Time-Series](https://mlsanity.com/paper/2410.02844/) (2024)
- [Coarse-to-Fine Learning of Dynamic Causal Structures](https://mlsanity.com/paper/2602.22532/) (2026)
- [Identifiable Markov Switching Models with Instantaneous Effects and Exponential Families](https://mlsanity.com/paper/2606.02231/) (2026)
- [Robust Causal Discovery in Real-World Time Series with Power-Laws](https://mlsanity.com/paper/2507.12257/) (2025)
- [Latent-Space Causal Discovery from Indirect Neuroimaging Observations](https://mlsanity.com/paper/2602.09034/) (2026)
- [Beyond Stationarity in Time Series: Discovering Causal Structures and Latent Regimes via Markov Blankets](https://mlsanity.com/paper/2609.05150/) (2026)
- [Concept Drift from a Causal Perspective](https://mlsanity.com/paper/2609.25340/) (2026)

## Abstract (arXiv)

Discovering causal relations from observational time series without making the stationary assumption is a significant challenge. In practice, this challenge is common in many areas, such as retail sales, transportation systems, and medical science. Here, we consider this problem for a class of non-stationary time series. The structural causal model (SCM) of this type of time series, called the semi-stationary time series, exhibits that a finite number of different causal mechanisms occur sequentially and periodically across time. This model holds considerable practical utility because it can represent periodicity, including common occurrences such as seasonality and diurnal variation. We propose a constraint-based, non-parametric algorithm for discovering causal relations in this setting. The resulting algorithm, PCMCIOmega, can capture the alternating and recurring changes in the causal mechanisms and then identify the underlying causal graph with conditional independence (CI) tests. We show that this algorithm is sound in identifying causal relations on discrete time series. We validate the algorithm with extensive experiments on continuous and discrete simulated data. We also apply our algorithm to a real-world climate dataset.