# TimeBridge: Non-Stationarity Matters for Long-term Time Series Forecasting

arXiv: https://arxiv.org/abs/2410.04442 · HTML: https://mlsanity.com/paper/2410.04442/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 57 references that are in the map.
- First posted on arXiv 6 Oct 2024.

## Builds on (most cited first, 30 of 30)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [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)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Long-term Forecasting with TiDE: Time-series Dense Encoder](https://mlsanity.com/paper/2304.08424/) (2023)
- [Financial Time Series Forecasting with Deep Learning : A Systematic Literature Review: 2005-2019](https://mlsanity.com/paper/1911.13288/) (2019)
- [TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods](https://mlsanity.com/paper/2403.20150/) (2024)
- [A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction](https://mlsanity.com/paper/1704.02971/) (2017)
- [Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors](https://mlsanity.com/paper/2305.18803/) (2023)
- [SparseTSF: Modeling Long-term Time Series Forecasting with 1k Parameters](https://mlsanity.com/paper/2405.00946/) (2024)
- [TimeCMA: Towards LLM-Empowered Multivariate Time Series Forecasting via Cross-Modality Alignment](https://mlsanity.com/paper/2406.01638/) (2024)
- [The Capacity and Robustness Trade-off: Revisiting the Channel Independent Strategy for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2304.05206/) (2023)
- [Dish-TS: A General Paradigm for Alleviating Distribution Shift in Time Series Forecasting](https://mlsanity.com/paper/2302.14829/) (2023)
- [Revitalizing Multivariate Time Series Forecasting: Learnable Decomposition with Inter-Series Dependencies and Intra-Series Variations Modeling](https://mlsanity.com/paper/2402.12694/) (2024)
- [A Unified Replay-based Continuous Learning Framework for Spatio-Temporal Prediction on Streaming Data](https://mlsanity.com/paper/2404.14999/) (2024)
- [Adaptive Multi-Scale Decomposition Framework for Time Series Forecasting](https://mlsanity.com/paper/2406.03751/) (2024)
- [Learning Multiple Stock Trading Patterns with Temporal Routing Adaptor and Optimal Transport](https://mlsanity.com/paper/2106.12950/) (2021)
- [Deep Frequency Derivative Learning for Non-stationary Time Series Forecasting](https://mlsanity.com/paper/2407.00502/) (2024)
- [U-Mixer: An Unet-Mixer Architecture with Stationarity Correction for Time Series Forecasting](https://mlsanity.com/paper/2401.02236/) (2024)

## Built on by (most cited first, 30 of 40)

- [Enhancing Time Series Forecasting through Selective Representation Spaces: A Patch Perspective](https://mlsanity.com/paper/2510.14510/) (2025)
- [Temporal Query Network for Efficient Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.12917/) (2025)
- [Aurora: Towards Universal Generative Multimodal Time Series Forecasting](https://mlsanity.com/paper/2509.22295/) (2025)
- [DistDF: Time-Series Forecasting Needs Joint-Distribution Wasserstein Alignment](https://mlsanity.com/paper/2510.24574/) (2025)
- [K2VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2505.23017/) (2025)
- [ASTGI: Adaptive Spatio-Temporal Graph Interactions for Irregular Multivariate Time Series Forecasting](https://mlsanity.com/paper/2509.23313/) (2025)
- [Learning General Causal Structures with Hidden Dynamic Process for Climate Analysis](https://mlsanity.com/paper/2501.12500/) (2025)
- [From Observations to States: Latent Time Series Forecasting](https://mlsanity.com/paper/2602.00297/) (2026)
- [PENGUIN: Enhancing Transformer with Periodic-Nested Group Attention for Long-term Time Series Forecasting](https://mlsanity.com/paper/2508.13773/) (2025)
- [FLAME: Flow Enhanced Legendre Memory Models for General Time Series Forecasting](https://mlsanity.com/paper/2512.14253/) (2025)
- [Task-Aware Mixture-of-Experts for Time Series Analysis](https://mlsanity.com/paper/2509.22279/) (2025)
- [Deep Time-series Forecasting Needs Kernelized Moment Balancing](https://mlsanity.com/paper/2602.00717/) (2026)
- [Routing Channel-Patch Dependencies in Time Series Forecasting with Graph Spectral Decomposition](https://mlsanity.com/paper/2603.13702/) (2026)
- [IndexNet: Timestamp and Variable-Aware Modeling for Time Series Forecasting](https://mlsanity.com/paper/2509.23813/) (2025)
- [How Effective Are Time-Series Models for Precipitation Nowcasting? A Comprehensive Benchmark for GNSS-based Precipitation Nowcasting](https://mlsanity.com/paper/2509.25263/) (2025)
- [LLM4Fluid: Large Language Models as Generalizable Neural Solvers for Fluid Dynamics](https://mlsanity.com/paper/2601.21681/) (2026)
- [To See Far, Look Close: Evolutionary Forecasting for Long-term Time Series](https://mlsanity.com/paper/2601.23114/) (2026)
- [InstanceRSR: Real-World Super-Resolution via Instance-Aware Representation Alignment](https://mlsanity.com/paper/2603.24240/) (2026)
- [Forecasting with Guidance: Representation-Level Supervision for Time Series Forecasting](https://mlsanity.com/paper/2603.24262/) (2026)
- [PAMNet: Cycle-aware Phase-Amplitude Modulation Network for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2605.02938/) (2026)
- [L-Drive: Beyond a Single Mapping-Latent Context Drives Time Series Forecasting](https://mlsanity.com/paper/2605.17730/) (2026)
- [Reviving Error Correction in Modern Deep Time-Series Forecasting](https://mlsanity.com/paper/2605.21088/) (2026)
- [Spectral Retrieval-Augmented Time-Series Forecasting](https://mlsanity.com/paper/2606.19412/) (2026)
- [Multivariate Time Series Forecasting needs Cross Variable Loss](https://mlsanity.com/paper/2608.05742/) (2026)
- [ReNF: Rethinking the Design of Neural Long-Term Time Series Forecasters](https://mlsanity.com/paper/2509.25914/) (2025)
- [Dual-Prototype Disentanglement: A Context-Aware Enhancement Framework for Time Series Forecasting](https://mlsanity.com/paper/2601.16632/) (2026)
- [Deep Time-Series Forecasting in 10 Years: A Survey](https://mlsanity.com/paper/2603.19899/) (2026)
- [Non-Stationarity in the Embedding Space of Time Series Foundation Models](https://mlsanity.com/paper/2604.16428/) (2026)
- [PAMod: Modeling Cyclical Shifts via Phase-Amplitude Modulation for Non-stationary Time Series Forecasting](https://mlsanity.com/paper/2605.00466/) (2026)
- [SeesawNet: Towards Non-stationary Time Series Forecasting with Balanced Modeling of Common and Specific Dependencies](https://mlsanity.com/paper/2605.14551/) (2026)

## Abstract (arXiv)

Non-stationarity poses significant challenges for multivariate time series forecasting due to the inherent short-term fluctuations and long-term trends that can lead to spurious regressions or obscure essential long-term relationships. Most existing methods either eliminate or retain non-stationarity without adequately addressing its distinct impacts on short-term and long-term modeling. Eliminating non-stationarity is essential for avoiding spurious regressions and capturing local dependencies in short-term modeling, while preserving it is crucial for revealing long-term cointegration across variates. In this paper, we propose TimeBridge, a novel framework designed to bridge the gap between non-stationarity and dependency modeling in long-term time series forecasting. By segmenting input series into smaller patches, TimeBridge applies Integrated Attention to mitigate short-term non-stationarity and capture stable dependencies within each variate, while Cointegrated Attention preserves non-stationarity to model long-term cointegration across variates. Extensive experiments show that TimeBridge consistently achieves state-of-the-art performance in both short-term and long-term forecasting. Additionally, TimeBridge demonstrates exceptional performance in financial forecasting on the CSI 500 and S&P 500 indices, further validating its robustness and effectiveness. Code is available at https://github.com/Hank0626/TimeBridge.