Research map / Time series / Long-term forecasting
S4M: S4 for multivariate time series forecasting with Missing values
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Proposes S4M, an end-to-end S4-based forecaster for multivariate time series with block missing values that uses a prototype bank (ATPM) and a mask-aware dual-stream S4 (MDS-S4) instead of two-step imputation.
Problem
Multivariate time series forecasting when data has block missing values at high missing ratios; two-step impute-then-forecast pipelines suffer error accumulation.
Approach
Integrates missing-data handling into the S4 latent space: a momentum-updated prototype bank retrieves representations of historical patterns for local statistics, and a dual-stream S4 takes the representation and an encoded missingness mask as separate inputs in the state-space recurrence.
Key results
- On Weather with time point missing (r=0.06, lookback 192), S4M reaches MSE 0.225, the best among compared methods.
- On Electricity with time point missing (r=0.06, lookback 96), S4M attains MAE 0.372 and MSE 0.287, competitive with the best Autoformer result (MSE 0.272 at lookback 96 is Autoformer's).
- Ablation shows removing the mask input increases errors on Weather under variable missing (e.g., MSE +0.520 at lookback 96).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add the mask input stream (ablation) | S4M · Variable missing, Electricity lookback 96 | MAE: +0.012 | Helped |
| add the mask input stream (ablation) | S4M · Variable missing, ETTh1 lookback 96 | MAE: -0.008 | Hurt |
| add ATPM (ablation) | S4M · Variable missing, Electricity lookback 96 | MAE: +0.011 | Helped |
| add ATPM (ablation) | S4M · Variable missing, ETTh1 lookback 96 | MAE: +0.044 | Helped |
| add the mask input stream (ablation) | S4M · Time point missing, Electricity lookback 96 | MAE: +0.014 | Helped |
| add ATPM (ablation) | S4M · Time point missing, Weather lookback 96 | MAE: +0.021 | Helped |
| increase initial prototype cluster count from 1 to 16 (ablation) | S4M · Electricity | MAE: 0.415 -> 0.415 | No clear effect |
| vary maximum prototype cluster count K1 (ablation) | S4M · Weather | MAE: 0.270; 0.267; 0.267; 0.268; 0.268 | No clear effect |
| vary prototypes per cluster K2 (ablation) | S4M · Electricity | MAE: 0.393; 0.377; 0.393; 0.398; 0.393; 0.394 | Mixed |
Surprising findings
- Autoformer (with mean imputation) beats S4M on several Electricity settings, e.g., MSE 0.272 vs 0.287 at lookback 96 under time point missing.
Limitations
- Evaluated only on four benchmark datasets with synthetic block missingness rather than naturally missing data.
- Results are mixed against Autoformer on some Electricity and Traffic settings, so claimed state-of-the-art is not uniform.
- Many hyperparameters (tau1, tau2, K1, K2) are set by hand and tuned on validation.
Experimental setup
Datasets: Electricity ETTh1 Traffic Weather
Benchmarks: Electricity ETTh1 Traffic Weather
Metrics: MSE MAE
Baselines: BRITS GRU-D Transformer Autoformer BiTGraph S4 (Mean) S4 (Ffill) S4 (Decay) S4 (SAITS)
Builds on: S4 GRU-D SAITS HiPPO
Closest papers by meaning
- BayOTIDE: Bayesian Online Multivariate Time Series Imputation with Functional Decomposition (ICML 2024 · similarity 0.87)
- Time-IMM: A Dataset and Benchmark for Irregular Multimodal Multivariate Time Series (NeurIPS 2025 · similarity 0.87)
- Time-MMD: Multi-Domain Multimodal Dataset for Time Series Analysis (NeurIPS 2024 · similarity 0.87)
- Chimera: Effectively Modeling Multivariate Time Series with 2-Dimensional State Space Models (NeurIPS 2024 · similarity 0.87)
- Frequency-aware Generative Models for Multivariate Time Series Imputation (NeurIPS 2024 · similarity 0.86)
- A Closer Look at Transformers for Time Series Forecasting: Understanding Why They Work and Where They Struggle (ICML 2025 · similarity 0.86)
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