# S4M: S4 for multivariate time series forecasting with Missing values

arXiv: https://arxiv.org/abs/2503.00900 · HTML: https://mlsanity.com/paper/2503.00900/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 39 references that are in the map.
- First posted on arXiv 2 Mar 2025.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [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)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction](https://mlsanity.com/paper/1704.02971/) (2017)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [Recurrent Neural Networks for Time Series Forecasting: Current Status and Future Directions](https://mlsanity.com/paper/1909.00590/) (2019)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [Temporal Pattern Attention for Multivariate Time Series Forecasting](https://mlsanity.com/paper/1809.04206/) (2018)
- [Is Mamba Effective for Time Series Forecasting?](https://mlsanity.com/paper/2403.11144/) (2024)
- [Modeling Irregular Time Series with Continuous Recurrent Units](https://mlsanity.com/paper/2111.11344/) (2021)
- [Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks](https://mlsanity.com/paper/2108.00298/) (2021)
- [Estimating Missing Data in Temporal Data Streams Using Multi-directional Recurrent Neural Networks](https://mlsanity.com/paper/1711.08742/) (2017)
- [Learning to Reconstruct Missing Data from Spatiotemporal Graphs with Sparse Observations](https://mlsanity.com/paper/2205.13479/) (2022)
- [CARD: Channel Aligned Robust Blend Transformer for Time Series Forecasting](https://mlsanity.com/paper/2305.12095/) (2023)
- [Scaleformer: Iterative Multi-scale Refining Transformers for Time Series Forecasting](https://mlsanity.com/paper/2206.04038/) (2022)
- [Joint Modeling of Local and Global Temporal Dynamics for Multivariate Time Series Forecasting with Missing Values](https://mlsanity.com/paper/1911.10273/) (2019)
- [Deep learning models for price forecasting of financial time series: A review of recent advancements: 2020-2022](https://mlsanity.com/paper/2305.04811/) (2023)
- [Hierarchical Memory Networks](https://mlsanity.com/paper/1605.07427/) (2016)
- [Recurrent Neural Filters: Learning Independent Bayesian Filtering Steps for Time Series Prediction](https://mlsanity.com/paper/1901.08096/) (2019)

## Built on by (most cited first, 6 of 6)

- [SciTS: Scientific Time Series Understanding and Generation with LLMs](https://mlsanity.com/paper/2510.03255/) (2025)
- [Revisiting Multivariate Time Series Forecasting with Missing Values](https://mlsanity.com/paper/2509.23494/) (2025)
- [Towards Robust Real-World Multivariate Time Series Forecasting: A Unified Framework for Dependency, Asynchrony, and Missingness](https://mlsanity.com/paper/2506.08660/) (2025)
- [CoIFNet: A Unified Framework for Multivariate Time Series Forecasting with Missing Values](https://mlsanity.com/paper/2506.13064/) (2025)
- [Alzheimers Disease Progression Prediction Based on Manifold Mapping of Irregularly Sampled Longitudinal Data](https://mlsanity.com/paper/2511.20154/) (2025)
- [Latent Laplace Diffusion for Irregular Multivariate Time Series](https://mlsanity.com/paper/2605.19805/) (2026)

## Abstract (arXiv)

Multivariate time series data play a pivotal role in a wide range of real-world applications. However, the presence of block missing data introduces significant challenges, often compromising the performance of predictive models. Traditional two-step approaches, which first impute missing values and then perform forecasting, are prone to error accumulation, particularly in complex multivariate settings characterized by high missing ratios and intricate dependency structures. In this work, we introduce S4M, an end-to-end time series forecasting framework that seamlessly integrates missing data handling into the Structured State Space Sequence (S4) model architecture. Unlike conventional methods that treat imputation as a separate preprocessing step, S4M leverages the latent space of S4 models to directly recognize and represent missing data patterns, thereby more effectively capturing the underlying temporal and multivariate dependencies. Our framework comprises two key components: the Adaptive Temporal Prototype Mapper (ATPM) and the Missing-Aware Dual Stream S4 (MDS-S4). The ATPM employs a prototype bank to derive robust and informative representations from historical data patterns, while the MDS-S4 processes these representations alongside missingness masks as dual input streams to enable accurate forecasting. Through extensive empirical evaluations on diverse real-world datasets, we demonstrate that S4M consistently achieves state-of-the-art performance. These results underscore the efficacy of our integrated approach in handling missing data, showcasing its robustness and superiority over traditional imputation-based methods. Our findings highlight the potential of S4M to advance reliable time series forecasting in practical applications, offering a promising direction for future research and deployment. Code is available at https://github.com/WINTERWEEL/S4M.git.