# The Capacity and Robustness Trade-off: Revisiting the Channel Independent Strategy for Multivariate Time Series Forecasting

arXiv: https://arxiv.org/abs/2304.05206 · HTML: https://mlsanity.com/paper/2304.05206/

## Key facts

- Cited by 101 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 58 references that are in the map.
- First posted on arXiv 11 Apr 2023.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [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)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [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)
- [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)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Robust Loss Functions under Label Noise for Deep Neural Networks](https://mlsanity.com/paper/1712.09482/) (2017)
- [Unsupervised Scalable Representation Learning for Multivariate Time Series](https://mlsanity.com/paper/1901.10738/) (2019)
- [Principles and Algorithms for Forecasting Groups of Time Series: Locality and Globality](https://mlsanity.com/paper/2008.00444/) (2020)
- [Making Risk Minimization Tolerant to Label Noise](https://mlsanity.com/paper/1403.3610/) (2014)
- [AutoCTS: Automated Correlated Time Series Forecasting -- Extended Version](https://mlsanity.com/paper/2112.11174/) (2021)
- [Do We Really Need Deep Learning Models for Time Series Forecasting?](https://mlsanity.com/paper/2101.02118/) (2021)
- [The Effectiveness of Discretization in Forecasting: An Empirical Study on Neural Time Series Models](https://mlsanity.com/paper/2005.10111/) (2020)
- [An Introduction to Temporal Graphs: An Algorithmic Perspective](https://mlsanity.com/paper/1503.00278/) (2015)

## Built on by (most cited first, 30 of 101)

- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [SparseTSF: Modeling Long-term Time Series Forecasting with 1k Parameters](https://mlsanity.com/paper/2405.00946/) (2024)
- [CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns](https://mlsanity.com/paper/2409.18479/) (2024)
- [CATCH: Channel-Aware multivariate Time Series Anomaly Detection via Frequency Patching](https://mlsanity.com/paper/2410.12261/) (2024)
- [VisionTS: Visual Masked Autoencoders Are Free-Lunch Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2408.17253/) (2024)
- [SOFTS: Efficient Multivariate Time Series Forecasting with Series-Core Fusion](https://mlsanity.com/paper/2404.14197/) (2024)
- [CARD: Channel Aligned Robust Blend Transformer for Time Series Forecasting](https://mlsanity.com/paper/2305.12095/) (2023)
- [SegRNN: Segment Recurrent Neural Network for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2308.11200/) (2023)
- [Revitalizing Multivariate Time Series Forecasting: Learnable Decomposition with Inter-Series Dependencies and Intra-Series Variations Modeling](https://mlsanity.com/paper/2402.12694/) (2024)
- [TimeBridge: Non-Stationarity Matters for Long-term Time Series Forecasting](https://mlsanity.com/paper/2410.04442/) (2024)
- [From Similarity to Superiority: Channel Clustering for Time Series Forecasting](https://mlsanity.com/paper/2404.01340/) (2024)
- [Learning to Embed Time Series Patches Independently](https://mlsanity.com/paper/2312.16427/) (2023)
- [Rethinking Channel Dependence for Multivariate Time Series Forecasting: Learning from Leading Indicators](https://mlsanity.com/paper/2401.17548/) (2024)
- [Temporal Query Network for Efficient Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.12917/) (2025)
- [Frequency-Aware Masked Autoencoders for Multimodal Pretraining on Biosignals](https://mlsanity.com/paper/2309.05927/) (2023)
- [PETformer: Long-term Time Series Forecasting via Placeholder-enhanced Transformer](https://mlsanity.com/paper/2308.04791/) (2023)
- [ST-MLP: A Cascaded Spatio-Temporal Linear Framework with Channel-Independence Strategy for Traffic Forecasting](https://mlsanity.com/paper/2308.07496/) (2023)
- [Parsimony or Capability? Decomposition Delivers Both in Long-term Time Series Forecasting](https://mlsanity.com/paper/2401.11929/) (2024)
- [FreEformer: Frequency Enhanced Transformer for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2501.13989/) (2025)
- [TimeDART: A Diffusion Autoregressive Transformer for Self-Supervised Time Series Representation](https://mlsanity.com/paper/2410.05711/) (2024)
- [Zero-shot Imputation with Foundation Inference Models for Dynamical Systems](https://mlsanity.com/paper/2402.07594/) (2024)
- [UniTST: Effectively Modeling Inter-Series and Intra-Series Dependencies for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2406.04975/) (2024)
- [MSHyper: Multi-Scale Hypergraph Transformer for Long-Range Time Series Forecasting](https://mlsanity.com/paper/2401.09261/) (2024)
- [VCformer: Variable Correlation Transformer with Inherent Lagged Correlation for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2405.11470/) (2024)
- [TimeDistill: Efficient Long-Term Time Series Forecasting with MLP via Cross-Architecture Distillation](https://mlsanity.com/paper/2502.15016/) (2025)
- [SageFormer: Series-Aware Framework for Long-term Multivariate Time Series Forecasting](https://mlsanity.com/paper/2307.01616/) (2023)
- [A Multi-Scale Decomposition MLP-Mixer for Time Series Analysis](https://mlsanity.com/paper/2310.11959/) (2023)
- [MCformer: Multivariate Time Series Forecasting with Mixed-Channels Transformer](https://mlsanity.com/paper/2403.09223/) (2024)
- [CMamba: Channel Correlation Enhanced State Space Models for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2406.05316/) (2024)
- [TFDNet: Time-Frequency Enhanced Decomposed Network for Long-term Time Series Forecasting](https://mlsanity.com/paper/2308.13386/) (2023)

## Abstract (arXiv)

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.