# MSGNet: Learning Multi-Scale Inter-Series Correlations for Multivariate Time Series Forecasting

arXiv: https://arxiv.org/abs/2401.00423 · HTML: https://mlsanity.com/paper/2401.00423/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 40 references that are in the map.
- First posted on arXiv 31 Dec 2023.

## Builds on (most cited first, 21 of 21)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [TS2Vec: Towards Universal Representation of Time Series](https://mlsanity.com/paper/2106.10466/) (2021)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [AI in Finance: Challenges, Techniques and Opportunities](https://mlsanity.com/paper/2107.09051/) (2021)
- [Towards Understanding Mixture of Experts in Deep Learning](https://mlsanity.com/paper/2208.02813/) (2022)
- [Spatiotemporal Propagation Learning for Network-Wide Flight Delay Prediction](https://mlsanity.com/paper/2207.06959/) (2022)

## Built on by (most cited first, 30 of 50)

- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretability](https://mlsanity.com/paper/2406.02496/) (2024)
- [A Comprehensive Survey of Deep Learning for Multivariate Time Series Forecasting: A Channel Strategy Perspective](https://mlsanity.com/paper/2502.10721/) (2025)
- [Temporal Query Network for Efficient Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.12917/) (2025)
- [ConvTimeNet: A Deep Hierarchical Fully Convolutional Model for Multivariate Time Series Analysis](https://mlsanity.com/paper/2403.01493/) (2024)
- [CrossLinear: Plug-and-Play Cross-Correlation Embedding for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2505.23116/) (2025)
- [Ada-MSHyper: Adaptive Multi-Scale Hypergraph Transformer for Time Series Forecasting](https://mlsanity.com/paper/2410.23992/) (2024)
- [Bridging Past and Future: Distribution-Aware Alignment for Time Series Forecasting](https://mlsanity.com/paper/2509.14181/) (2025)
- [Out-of-Distribution Generalization in Time Series: A Survey](https://mlsanity.com/paper/2503.13868/) (2025)
- [MSHyper: Multi-Scale Hypergraph Transformer for Long-Range Time Series Forecasting](https://mlsanity.com/paper/2401.09261/) (2024)
- [Vision-Enhanced Time Series Forecasting via Latent Diffusion Models](https://mlsanity.com/paper/2502.14887/) (2025)
- [Learning General Causal Structures with Hidden Dynamic Process for Climate Analysis](https://mlsanity.com/paper/2501.12500/) (2025)
- [NuwaTS: a Foundation Model Mending Every Incomplete Time Series](https://mlsanity.com/paper/2405.15317/) (2024)
- [ForecastGrapher: Redefining Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2405.18036/) (2024)
- [A Survey of Spatio-Temporal EEG data Analysis: from Models to Applications](https://mlsanity.com/paper/2410.08224/) (2024)
- [Beyond Fixed Variables: Expanding-variate Time Series Forecasting via Flat Scheme and Spatio-temporal Focal Learning](https://mlsanity.com/paper/2502.15296/) (2025)
- [Evaluating Temporal Plasticity in Foundation Time Series Models for Incremental Fine-tuning](https://mlsanity.com/paper/2504.14677/) (2025)
- [Representation Learning of Limit Order Book: A Comprehensive Study and Benchmarking](https://mlsanity.com/paper/2505.02139/) (2025)
- [ST-Hyper: Learning High-Order Dependencies Across Multiple Spatial-Temporal Scales for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2509.02217/) (2025)
- [MillGNN: Learning Multi-Scale Lead-Lag Dependencies for Multi-Variate Time Series Forecasting](https://mlsanity.com/paper/2509.03852/) (2025)
- [Routing Channel-Patch Dependencies in Time Series Forecasting with Graph Spectral Decomposition](https://mlsanity.com/paper/2603.13702/) (2026)
- [PULSE: Generative Phase Evolution for Non-Stationary Time Series Forecasting](https://mlsanity.com/paper/2605.16793/) (2026)
- [Robust Multivariate Time Series Forecasting against Intra- and Inter-Series Transitional Shift](https://mlsanity.com/paper/2407.13194/) (2024)
- [Ister: Linear Transformer for Efficient Multivariate Time Series Forecasting](https://mlsanity.com/paper/2412.18798/) (2024)
- [SEED: A Structural Encoder for Embedding-Driven Decoding in Time Series Prediction with LLMs](https://mlsanity.com/paper/2506.20167/) (2025)
- [Detecting Multilevel Manipulation from Limit Order Book via Cascaded Contrastive Representation Learning](https://mlsanity.com/paper/2508.17086/) (2025)
- [SDGF: Fusing Static and Multi-Scale Dynamic Correlations for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2509.18135/) (2025)
- [WDformer: A Wavelet-based Differential Transformer Model for Time Series Forecasting](https://mlsanity.com/paper/2509.25231/) (2025)
- [How Effective Are Time-Series Models for Precipitation Nowcasting? A Comprehensive Benchmark for GNSS-based Precipitation Nowcasting](https://mlsanity.com/paper/2509.25263/) (2025)
- [TimePerceiver: An Encoder-Decoder Framework for Generalized Time-Series Forecasting](https://mlsanity.com/paper/2512.22550/) (2025)

## Abstract (arXiv)

Multivariate time series forecasting poses an ongoing challenge across various disciplines. Time series data often exhibit diverse intra-series and inter-series correlations, contributing to intricate and interwoven dependencies that have been the focus of numerous studies. Nevertheless, a significant research gap remains in comprehending the varying inter-series correlations across different time scales among multiple time series, an area that has received limited attention in the literature. To bridge this gap, this paper introduces MSGNet, an advanced deep learning model designed to capture the varying inter-series correlations across multiple time scales using frequency domain analysis and adaptive graph convolution. By leveraging frequency domain analysis, MSGNet effectively extracts salient periodic patterns and decomposes the time series into distinct time scales. The model incorporates a self-attention mechanism to capture intra-series dependencies, while introducing an adaptive mixhop graph convolution layer to autonomously learn diverse inter-series correlations within each time scale. Extensive experiments are conducted on several real-world datasets to showcase the effectiveness of MSGNet. Furthermore, MSGNet possesses the ability to automatically learn explainable multi-scale inter-series correlations, exhibiting strong generalization capabilities even when applied to out-of-distribution samples.