# Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets

arXiv: https://arxiv.org/abs/2003.03685 · HTML: https://mlsanity.com/paper/2003.03685/

## Key facts

- Cited by 137 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Mar 2020.

## Built on by (most cited first, 30 of 137)

- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Causal Inference for Time series Analysis: Problems, Methods and Evaluation](https://mlsanity.com/paper/2102.05829/) (2021)
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- [CausalTime: Realistically Generated Time-series for Benchmarking of Causal Discovery](https://mlsanity.com/paper/2310.01753/) (2023)
- [A Survey on Causal Discovery Methods for I.I.D. and Time Series Data](https://mlsanity.com/paper/2303.15027/) (2023)
- [NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledge](https://mlsanity.com/paper/2109.04286/) (2021)
- [Rhino: Deep Causal Temporal Relationship Learning With History-dependent Noise](https://mlsanity.com/paper/2210.14706/) (2022)
- [Root Cause Identification for Collective Anomalies in Time Series given an Acyclic Summary Causal Graph with Loops](https://mlsanity.com/paper/2303.04038/) (2023)
- [Data Generating Process to Evaluate Causal Discovery Techniques for Time Series Data](https://mlsanity.com/paper/2104.08043/) (2021)
- [Achieving Long-Term Fairness in Sequential Decision Making](https://mlsanity.com/paper/2204.01819/) (2022)
- [Hierarchical Graph Neural Networks for Causal Discovery and Root Cause Localization](https://mlsanity.com/paper/2302.01987/) (2023)
- [Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes](https://mlsanity.com/paper/2402.18477/) (2024)
- [AI for IT Operations (AIOps) on Cloud Platforms: Reviews, Opportunities and Challenges](https://mlsanity.com/paper/2304.04661/) (2023)
- [Structural Hawkes Processes for Learning Causal Structure from Discrete-Time Event Sequences](https://mlsanity.com/paper/2305.05986/) (2023)
- [Case Studies of Causal Discovery from IT Monitoring Time Series](https://mlsanity.com/paper/2307.15678/) (2023)
- [Neural Structure Learning with Stochastic Differential Equations](https://mlsanity.com/paper/2311.03309/) (2023)
- [RealTCD: Temporal Causal Discovery from Interventional Data with Large Language Model](https://mlsanity.com/paper/2404.14786/) (2024)
- [The Causal Chambers: Real Physical Systems as a Testbed for AI Methodology](https://mlsanity.com/paper/2404.11341/) (2024)
- [Discovering Mixtures of Structural Causal Models from Time Series Data](https://mlsanity.com/paper/2310.06312/) (2023)
- [TimeGraph: Synthetic Benchmark Datasets for Robust Time-Series Causal Discovery](https://mlsanity.com/paper/2506.01361/) (2025)
- [Separation-based distance measures for causal graphs](https://mlsanity.com/paper/2402.04952/) (2024)
- [Causal Discovery from Time Series with Hybrids of Constraint-Based and Noise-Based Algorithms](https://mlsanity.com/paper/2306.08765/) (2023)
- [Bootstrap aggregation and confidence measures to improve time series causal discovery](https://mlsanity.com/paper/2306.08946/) (2023)
- [CausalDynamics: A large-scale benchmark for structural discovery of dynamical causal models](https://mlsanity.com/paper/2505.16620/) (2025)
- [Multiscale Causal Structure Learning](https://mlsanity.com/paper/2207.07908/) (2022)
- [CDANs: Temporal Causal Discovery from Autocorrelated and Non-Stationary Time Series Data](https://mlsanity.com/paper/2302.03246/) (2023)
- [Learning General Causal Structures with Hidden Dynamic Process for Climate Analysis](https://mlsanity.com/paper/2501.12500/) (2025)
- [Interventional Time Series Priors for Causal Foundation Models](https://mlsanity.com/paper/2603.11090/) (2026)

## Abstract (arXiv)

The paper introduces a novel conditional independence (CI) based method for linear and nonlinear, lagged and contemporaneous causal discovery from observational time series in the causally sufficient case. Existing CI-based methods such as the PC algorithm and also common methods from other frameworks suffer from low recall and partially inflated false positives for strong autocorrelation which is an ubiquitous challenge in time series. The novel method, PCMCI^+, extends PCMCI [Runge et al., 2019b] to include discovery of contemporaneous links. PCMCI^+ improves the reliability of CI tests by optimizing the choice of conditioning sets and even benefits from autocorrelation. The method is order-independent and consistent in the oracle case. A broad range of numerical experiments demonstrates that PCMCI^+ has higher adjacency detection power and especially more contemporaneous orientation recall compared to other methods while better controlling false positives. Optimized conditioning sets also lead to much shorter runtimes than the PC algorithm. PCMCI^+ can be of considerable use in many real world application scenarios where often time resolutions are too coarse to resolve time delays and strong autocorrelation is present.