# Variable-lag Granger Causality and Transfer Entropy for Time Series Analysis

arXiv: https://arxiv.org/abs/2002.00208 · HTML: https://mlsanity.com/paper/2002.00208/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Feb 2020.

## Built on by (most cited first, 9 of 9)

- [Multi-Scale Adaptive Graph Neural Network for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2201.04828/) (2022)
- [Auto IV: Counterfactual Prediction via Automatic Instrumental Variable Decomposition](https://mlsanity.com/paper/2107.05884/) (2021)
- [Causal Feature Selection via Transfer Entropy](https://mlsanity.com/paper/2310.11059/) (2023)
- [CTP:A Causal Interpretable Model for Non-Communicable Disease Progression Prediction](https://mlsanity.com/paper/2308.09735/) (2023)
- [Framework for inferring empirical causal graphs from binary data to support multidimensional poverty analysis](https://mlsanity.com/paper/2205.06131/) (2022)
- [Identifying Time Lag in Dynamical Systems with Copula Entropy based Transfer Entropy](https://mlsanity.com/paper/2301.06037/) (2023)
- [Framework for Variable-lag Motif Following Relation Inference In Time Series using Matrix Profile analysis](https://mlsanity.com/paper/2401.02860/) (2024)
- [MotifDisco: Motif Causal Discovery For Time Series Motifs](https://mlsanity.com/paper/2409.15219/) (2024)
- [Reasoning-based Anomaly Detection Framework: A Real-time, Scalable, and Automated Approach to Anomaly Detection Across Domains](https://mlsanity.com/paper/2510.03486/) (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. The assumption of fixed time delay also exists in Transfer Entropy, which is considered to be a non-linear version of Granger causality. 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 and Variable-lag Transfer Entropy, generalizations of both Granger causality and Transfer Entropy that relax the assumption of the fixed time delay and allow causes to influence effects with arbitrary time delays. In addition, we propose methods for inferring both variable-lag Granger causality and Transfer Entropy relations. In our approaches, we utilize an optimal warping path of Dynamic Time Warping (DTW) to infer variable-lag causal relations. We demonstrate our approaches on an application for studying coordinated collective behavior and other real-world casual-inference datasets and show that our proposed approaches perform better than several existing methods in both simulated and real-world datasets. Our approaches can be applied in any domain of time series analysis. The software of this work is available in the R-CRAN package: VLTimeCausality.