# Leveraging Multivariate Long-Term History Representation for Time Series Forecasting

arXiv: https://arxiv.org/abs/2505.14737 · HTML: https://mlsanity.com/paper/2505.14737/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 56 references that are in the map.
- First posted on arXiv 20 May 2025.

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing](https://mlsanity.com/paper/1905.00067/) (2019)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [Discrete Graph Structure Learning for Forecasting Multiple Time Series](https://mlsanity.com/paper/2101.06861/) (2021)
- [Dynamic Graph Convolutional Recurrent Network for Traffic Prediction: Benchmark and Solution](https://mlsanity.com/paper/2104.14917/) (2021)
- [Spatial-Temporal Identity: A Simple yet Effective Baseline for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2208.05233/) (2022)
- [Decoupled Dynamic Spatial-Temporal Graph Neural Network for Traffic Forecasting](https://mlsanity.com/paper/2206.09112/) (2022)
- [Pre-training Enhanced Spatial-temporal Graph Neural Network for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2206.09113/) (2022)
- [Multi-Scale Adaptive Graph Neural Network for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2201.04828/) (2022)
- [Learning the Evolutionary and Multi-scale Graph Structure for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2206.13816/) (2022)
- [Nearest Neighbor Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.11625/) (2025)

## Built on by (most cited first, 1 of 1)

- [STEMS: Spatial-Temporal Enhanced Safe Multi-Agent Coordination for Building Energy Management](https://mlsanity.com/paper/2510.14112/) (2025)

## Abstract (arXiv)

Multivariate Time Series (MTS) forecasting has a wide range of applications in both industry and academia. Recent advances in Spatial-Temporal Graph Neural Network (STGNN) have achieved great progress in modelling spatial-temporal correlations. Limited by computational complexity, most STGNNs for MTS forecasting focus primarily on short-term and local spatial-temporal dependencies. Although some recent methods attempt to incorporate univariate history into modeling, they still overlook crucial long-term spatial-temporal similarities and correlations across MTS, which are essential for accurate forecasting. To fill this gap, we propose a framework called the Long-term Multivariate History Representation (LMHR) Enhanced STGNN for MTS forecasting. Specifically, a Long-term History Encoder (LHEncoder) is adopted to effectively encode the long-term history into segment-level contextual representations and reduce point-level noise. A non-parametric Hierarchical Representation Retriever (HRetriever) is designed to include the spatial information in the long-term spatial-temporal dependency modelling and pick out the most valuable representations with no additional training. A Transformer-based Aggregator (TAggregator) selectively fuses the sparsely retrieved contextual representations based on the ranking positional embedding efficiently. Experimental results demonstrate that LMHR outperforms typical STGNNs by 10.72% on the average prediction horizons and state-of-the-art methods by 4.12% on several real-world datasets. Additionally, it consistently improves prediction accuracy by 9.8% on the top 10% of rapidly changing patterns across the datasets.