  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.
