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.

多元时间序列预测：提出了Variable Correlation Transformer (VCformer)模型，通过Variable Correlation Attention (VCA)模块挖掘变量之间的相关性，并结合Koopman Temporal Detector (KTD)来处理时间序列的非平稳性，实验证明VCformer在真实数据集上取得了优异的性能。

VCformer：具有内在滞后相关性的多元时间序列预测中的变量相关变压器