# Multivariate Time Series Forecasting with Transfer Entropy Graph

arXiv: https://arxiv.org/abs/2005.01185 · HTML: https://mlsanity.com/paper/2005.01185/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 May 2020.

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

- [Scale-Aware Neural Architecture Search for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2112.07459/) (2021)
- [A Systematic Literature Review of Spatio-Temporal Graph Neural Network Models for Time Series Forecasting and Classification](https://mlsanity.com/paper/2410.22377/) (2024)
- [Entropy Causal Graphs for Multivariate Time Series Anomaly Detection](https://mlsanity.com/paper/2312.09478/) (2023)
- [Structural Knowledge Informed Continual Multivariate Time Series Forecasting](https://mlsanity.com/paper/2402.12722/) (2024)
- [Applications of Entropy in Data Analysis and Machine Learning: A Review](https://mlsanity.com/paper/2503.02921/) (2025)
- [Refined Causal Graph Structure Learning via Curvature for Brain Disease Classification](https://mlsanity.com/paper/2506.15708/) (2025)
- [Transfer Entropy in Graph Convolutional Neural Networks](https://mlsanity.com/paper/2406.06632/) (2024)
- [Introducing Diminutive Causal Structure into Graph Representation Learning](https://mlsanity.com/paper/2406.08709/) (2024)
- [MotifDisco: Motif Causal Discovery For Time Series Motifs](https://mlsanity.com/paper/2409.15219/) (2024)
- [Causal and Local Correlations Based Network for Multivariate Time Series Classification](https://mlsanity.com/paper/2411.18008/) (2024)

## Abstract (arXiv)

Multivariate time series (MTS) forecasting is an essential problem in many fields. Accurate forecasting results can effectively help decision-making. To date, many MTS forecasting methods have been proposed and widely applied. However, these methods assume that the predicted value of a single variable is affected by all other variables, which ignores the causal relationship among variables. To address the above issue, we propose a novel end-to-end deep learning model, termed graph neural network with Neural Granger Causality (CauGNN) in this paper. To characterize the causal information among variables, we introduce the Neural Granger Causality graph in our model. Each variable is regarded as a graph node, and each edge represents the casual relationship between variables. In addition, convolutional neural network (CNN) filters with different perception scales are used for time series feature extraction, which is used to generate the feature of each node. Finally, Graph Neural Network (GNN) is adopted to tackle the forecasting problem of graph structure generated by MTS. Three benchmark datasets from the real world are used to evaluate the proposed CauGNN. The comprehensive experiments show that the proposed method achieves state-of-the-art results in the MTS forecasting task.