Multivariate time series data comprises various channels of variables. The multivariate forecasting models need to capture the relationship between the channels to accurately predict future values. However, recently, there has been an emergence of methods that employ the Channel Independent (CI) strategy. These methods view multivariate time series data as separate univariate time series and disregard the correlation between channels. Surprisingly, our empirical results have shown that models trained with the CI strategy outperform those trained with the Channel Dependent (CD) strategy, usually by a significant margin. Nevertheless, the reasons behind this phenomenon have not yet been thoroughly explored in the literature. This paper provides comprehensive empirical and theoretical analyses of the characteristics of multivariate time series datasets and the CI/CD strategy. Our results conclude that the CD approach has higher capacity but often lacks robustness to accurately predict distributionally drifted time series. In contrast, the CI approach trades capacity for robust prediction. Practical measures inspired by these analyses are proposed to address the capacity and robustness dilemma, including a modified CD method called Predict Residuals with Regularization (PRReg) that can surpass the CI strategy. We hope our findings can raise awareness among researchers about the characteristics of multivariate time series and inspire the construction of better forecasting models.

翻译：多变量时间序列数据包含多个变量通道。多变量预测模型需要捕捉通道之间的关系以准确预测未来值。然而，近期出现了一系列采用通道独立（CI）策略的方法。这些方法将多变量时间序列数据视为独立的单变量时间序列，忽略了通道之间的相关性。令人惊讶的是，我们的实证结果表明，采用CI策略训练的模型通常以显著优势优于采用通道依赖（CD）策略训练的模型。尽管如此，文献中尚未深入探讨这一现象背后的原因。本文对多变量时间序列数据集及CI/CD策略的特性进行了全面的实证与理论分析。研究结论表明，CD方法具有更高的容量，但在准确预测分布漂移的时间序列时往往缺乏鲁棒性。相比之下，CI方法通过牺牲容量换取鲁棒预测。基于这些分析，本文提出解决容量与鲁棒性困境的实用措施，包括一种名为带有正则化的残差预测（PRReg）的改进CD方法，该方法可超越CI策略。我们期望这项发现能提高研究者对多变量时间序列特性的认识，并启发构建更优的预测模型。