# Variable-lag Granger Causality for Time Series Analysis

arXiv: https://arxiv.org/abs/1912.10829 · HTML: https://mlsanity.com/paper/1912.10829/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2019.

## Built on by (most cited first, 10 of 10)

- [AI in Finance: Challenges, Techniques and Opportunities](https://mlsanity.com/paper/2107.09051/) (2021)
- [Causal Inference for Time series Analysis: Problems, Methods and Evaluation](https://mlsanity.com/paper/2102.05829/) (2021)
- [Rhino: Deep Causal Temporal Relationship Learning With History-dependent Noise](https://mlsanity.com/paper/2210.14706/) (2022)
- [Beyond Predictions in Neural ODEs: Identification and Interventions](https://mlsanity.com/paper/2106.12430/) (2021)
- [Neural Structure Learning with Stochastic Differential Equations](https://mlsanity.com/paper/2311.03309/) (2023)
- [Causal Temporal Regime Structure Learning](https://mlsanity.com/paper/2311.01412/) (2023)
- [Robust Causality and False Attribution in Data-Driven Earth Science Discoveries](https://mlsanity.com/paper/2209.12580/) (2022)
- [Hawkes Processes with Delayed Granger Causality](https://mlsanity.com/paper/2308.06106/) (2023)
- [Transformers with Sparse Attention for Granger Causality](https://mlsanity.com/paper/2411.13264/) (2024)
- [A Self-explainable Model of Long Time Series by Extracting Informative Structured Causal Patterns](https://mlsanity.com/paper/2512.01412/) (2025)

## Abstract (arXiv)

Granger causality is a fundamental technique for causal inference in time series data, commonly used in the social and biological sciences. Typical operationalizations of Granger causality make a strong assumption that every time point of the effect time series is influenced by a combination of other time series with a fixed time delay. However, the assumption of the fixed time delay does not hold in many applications, such as collective behavior, financial markets, and many natural phenomena. To address this issue, we develop variable-lag Granger causality, a generalization of Granger causality that relaxes the assumption of the fixed time delay and allows causes to influence effects with arbitrary time delays. In addition, we propose a method for inferring variable-lag Granger causality relations. We demonstrate our approach on an application for studying coordinated collective behavior and show that it performs better than several existing methods in both simulated and real-world datasets. Our approach can be applied in any domain of time series analysis.