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A Comprehensive Survey of Deep Learning for Multivariate Time Series Forecasting: A Channel Strategy Perspective
Xiangfei Qiu, Hanyin Cheng, Xingjian Wu, Junkai Lu, Jilin Hu, Chenjuan Guo, Christian S. Jensen, Bin Yang
TL;DR
MTSF requires effective modeling of correlations among channels, but existing surveys provide limited comprehensive discussion of channel strategies. This survey organizes deep learning approaches into a three-level taxonomy, analyzes their mechanisms and characteristics, and compares their strengths and limitations. It concludes with future research directions for channel-strategy-based MTSF.
Problem
Existing MTSF surveys often lack a comprehensive discussion of channel strategies, despite the importance of channel correlations for prediction accuracy.
Method
The survey categorizes channel strategies across strategy, mechanism, and characteristic perspectives, then reviews representative methods and compares their advantages and limitations.
Results
The survey provides a structured understanding of channel strategies and reports that CI performs better under weak correlations, while CP generalizes best as correlations strengthen.
Takeaways & Limitations
Channel-strategy choice should account for inter-channel correlation strength, with partial dependence offering flexible interaction modeling while filtering noise in strongly correlated settings.
Takeaways & Limitations
Few models address correlations within the prediction horizon, and existing approaches targeting them focus on short-term forecasting and are difficult to scale to long-term forecasting.
Abstract
from arXiv · showhide
Multivariate Time Series Forecasting (MTSF) plays a crucial role across diverse fields, ranging from economic, energy, to traffic. In recent years, deep learning has demonstrated outstanding performance in MTSF tasks. In MTSF, modeling the correlations among different channels is critical, as leveraging information from other related channels can significantly improve the prediction accuracy of a specific channel. This study systematically reviews the channel modeling strategies for time series and proposes a taxonomy organized into three hierarchical levels: the strategy perspective, the mechanism perspective, and the characteristic perspective. On this basis, we provide a structured analysis of these methods and conduct an in-depth examination of the advantages and limitations of different channel strategies. Finally, we summarize and discuss some future research directions to provide useful research guidance. Moreover, we maintain an up-to-date Github repository (https://github.com/decisionintelligence/CS4TS) which includes all the papers discussed in the survey.
1 Introduction
MTSF depends on modeling relationships among channels, yet existing surveys have not comprehensively addressed channel strategies. This survey introduces a three-level taxonomy and reviews strategy developments, strengths, limitations, and future directions.
- Motivation: MTSF predicts multiple interdependent channels across economic, energy, and traffic applications.Accurate forecasts support informed decisions, resource allocation, and operational efficiency.
- Motivation: Modeling channel correlations can improve prediction accuracy by leveraging information from related channels.Financial forecasting can combine stock prices, trading volumes, and market indices to capture market dynamics.
- Channel strategies: Existing channel strategies comprise Channel Independence, Channel Dependence, and a partially described third category in the overview.The survey frames channel-strategy selection as a key design consideration for MTSF.
- Survey scope: The survey addresses limited channel-strategy coverage in prior MTSF surveys through a taxonomy spanning strategy, mechanism, and characteristic perspectives.It systematically introduces strategy definitions and representative methods, then examines implementation mechanisms and modeled channel characteristics.
- Contributions: The survey provides an up-to-date review, a structured channel-strategy taxonomy, analysis of strengths and limitations, and future research opportunities.Its contributions emphasize deep learning models for MTSF and channel-strategy development.
2 Preliminaries
The preliminaries define a time series as a sequence of multichannel time points and formulate MTSF as predicting future points from historical observations.
- Time Series: A time series X ∈ R^T×N is a time-oriented sequence of N-dimensional points, with T timestamps and N channels.
- Multivariate Time Series Forecasting: MTSF predicts the next F time points Y ∈ R^F×N from a historical series X ∈ R^T×N, where F is the forecasting horizon.
3 Taxonomy of Channel Strategies in MTSF
The taxonomy organizes MTSF channel strategies across strategy, mechanism, and characteristic perspectives, linking how channels interact to the mechanisms and correlation properties being modeled.
- Taxonomy overview: The taxonomy has three hierarchical levels: strategy, mechanism, and characteristic perspectives.It provides a structured classification for understanding channel strategies in MTSF.
- Strategy perspective: Channel strategies process, integrate, or utilize information from multiple input channels.The strategy perspective examines how multivariate channel information is handled.
- Strategy perspective: Channel Independence processes each channel separately, whereas Channel Partiality preserves channel independence while selectively interacting with related channels.Partial interactions may use fixed or dynamically changing sets of related channels.
- Mechanism perspective: Transformer-based mechanisms use global modeling, while MLP and CNN mechanisms capture channel correlations through feature mixing or weighted convolutional merging.MLP Mixing models all-channel correlations through fully connected layers, whereas CNN Merging combines channel features during convolution.
- Mechanism perspective: GNN-based mechanisms represent channels as graph nodes and their correlations as edges, with graph sparsity distinguishing CD from CP strategies.Simple graphs can use time- or frequency-domain information to learn channel relationships.
- Characteristic perspective: The characteristic perspective examines correlation properties including lagginess, polarity, and multi-scale behavior.These characteristics describe delayed cross-channel effects, positive or negative interactions, and correlation changes across time scales.
4 Comparison within the Taxonomy
The comparison evaluates CI, CD, and CP across correlation strength and computational cost. CI is efficient and effective under weak correlations, while CD and CP perform better as correlations strengthen, with CP showing the strongest generalization.
- Performance across Correlation: CI performs best in weakly correlated scenarios by disregarding inter-channel noise, while CD can overfit spurious correlations.
- Performance across Correlation: As correlations strengthen, CI encounters a capacity bottleneck, whereas CD and CP achieve stronger predictive performance.
- Performance across Correlation: CP demonstrates the strongest generalization by modeling complex inter-channel dependencies while filtering noise.
- Efficiency and Computational Complexity: CI minimizes parameter counts and inference latency by decoupling channels and sharing weights across univariate processes.
- Efficiency and Computational Complexity: CD and CP incur substantially higher parameter counts and inference costs because they explicitly model inter-channel dependencies.
5 Future Research Opportunities
Future research should address channel correlations within the prediction horizon, richer correlation characteristics, and multimodal information. The survey also notes that current foundation-model approaches commonly favor channel independence because of modality and channel-count constraints.
- 5.1 Channel Correlation in Future Horizon: Few models address channel correlations within the prediction horizon, and existing approaches are difficult to scale to long-term forecasting.
- 5.2 Other Correlation Characteristics: Future work could model channel correlations separately within trend and seasonal components and integrate them across components.
- 5.2 Other Correlation Characteristics: Correlations may differ across frequency components, motivating further study of multi-frequency channel characteristics.
- 5.3 Multimodal Data: Multimodal data such as text, images, and sensor data could provide richer information for modeling channel correlations.
- 5.4 Foundation Models: LLM-based and many time-series pre-trained foundation models typically adopt channel independence because language lacks channels and time-series channel counts are heterogeneous.
6 Conclusion
The survey reviews deep learning methods for MTSF through a channel-strategy perspective, organizing approaches with a methodological taxonomy. It also synthesizes strategy strengths and limitations and identifies future research directions.
- The survey provides a comprehensive review of deep learning methods for MTSF from a channel strategy perspective.
- It categorizes and summarizes existing approaches using a methodological taxonomy to structure understanding of the field.
- The survey discusses strengths and limitations of channel strategies and outlines future research directions for MTSF.