# VCformer: Variable Correlation Transformer with Inherent Lagged Correlation for Multivariate Time Series Forecasting

arXiv: https://arxiv.org/abs/2405.11470 · HTML: https://mlsanity.com/paper/2405.11470/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 42 references that are in the map.
- First posted on arXiv 19 May 2024.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting](https://mlsanity.com/paper/1905.03806/) (2019)
- [Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors](https://mlsanity.com/paper/2305.18803/) (2023)
- [The Capacity and Robustness Trade-off: Revisiting the Channel Independent Strategy for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2304.05206/) (2023)
- [Learning Compositional Koopman Operators for Model-Based Control](https://mlsanity.com/paper/1910.08264/) (2019)
- [DSformer: A Double Sampling Transformer for Multivariate Time Series Long-term Prediction](https://mlsanity.com/paper/2308.03274/) (2023)
- [Deep Learning of Koopman Representation for Control](https://mlsanity.com/paper/2010.07546/) (2020)
- [Compressed Interaction Graph based Framework for Multi-behavior Recommendation](https://mlsanity.com/paper/2303.02418/) (2023)

## Built on by (most cited first, 12 of 12)

- [A Comprehensive Survey of Deep Learning for Multivariate Time Series Forecasting: A Channel Strategy Perspective](https://mlsanity.com/paper/2502.10721/) (2025)
- [CC-Time: Cross-Model and Cross-Modality Time Series Forecasting](https://mlsanity.com/paper/2508.12235/) (2025)
- [Sequential Order-Robust Mamba for Time Series Forecasting](https://mlsanity.com/paper/2410.23356/) (2024)
- [From Text to Forecasts: Bridging Modality Gap with Temporal Evolution Semantic Space](https://mlsanity.com/paper/2603.12664/) (2026)
- [TiVaT: A Transformer with a Single Unified Mechanism for Capturing Asynchronous Dependencies in Multivariate Time Series Forecasting](https://mlsanity.com/paper/2410.01531/) (2024)
- [A Comparative Study of Pruning Methods in Transformer-based Time Series Forecasting](https://mlsanity.com/paper/2412.12883/) (2024)
- [Towards Robust Real-World Multivariate Time Series Forecasting: A Unified Framework for Dependency, Asynchrony, and Missingness](https://mlsanity.com/paper/2506.08660/) (2025)
- [What If We Let Forecasting Forget? A Sparse Bottleneck for Cross-Variable Dependencies](https://mlsanity.com/paper/2605.08289/) (2026)
- [CRAFT: Time Series Forecasting with Cross-Future Behavior Awareness](https://mlsanity.com/paper/2505.13896/) (2025)
- [Tailored Architectures for Time Series Forecasting: Evaluating Deep Learning Models on Gaussian Process-Generated Data](https://mlsanity.com/paper/2506.08977/) (2025)
- [CrossLag: Predicting Major Dengue Outbreaks with a Domain Knowledge Informed Transformer](https://mlsanity.com/paper/2510.03566/) (2025)
- [InvDec: Inverted Decoder for Multivariate Time Series Forecasting with Separated Temporal and Variate Modeling](https://mlsanity.com/paper/2510.20302/) (2025)

## Abstract (arXiv)

Multivariate time series (MTS) forecasting has been extensively applied across diverse domains, such as weather prediction and energy consumption. However, current studies still rely on the vanilla point-wise self-attention mechanism to capture cross-variable dependencies, which is inadequate in extracting the intricate cross-correlation implied between variables. To fill this gap, we propose Variable Correlation Transformer (VCformer), which utilizes Variable Correlation Attention (VCA) module to mine the correlations among variables. Specifically, based on the stochastic process theory, VCA calculates and integrates the cross-correlation scores corresponding to different lags between queries and keys, thereby enhancing its ability to uncover multivariate relationships. Additionally, inspired by Koopman dynamics theory, we also develop Koopman Temporal Detector (KTD) to better address the non-stationarity in time series. The two key components enable VCformer to extract both multivariate correlations and temporal dependencies. Our extensive experiments on eight real-world datasets demonstrate the effectiveness of VCformer, achieving top-tier performance compared to other state-of-the-art baseline models. Code is available at this repository: https://github.com/CSyyn/VCformer.