Understanding Key Features of Time Series Foundation Models from Epidemic Forecasting

Abstract: Seasonal influenza infects millions of people and causes substantial morbidity and mortality in the United States each year, making accurate short-term forecasting a core public-health need. Reliable forecasts of epidemic time series can inform vaccination timing, hospital staffing, and resource allocation, yet the comparative behavior of modern forecasting architectures on infectious-disease surveillance data remains insufficiently characterized. We address this gap through a systematic evaluation of regional influenza forecasting using influenza-like illness surveillance and influenza-associated hospitalization time series under both temporal and spatial generalization settings for 1-4-week-ahead prediction. We compare classical neural network architectures, numerical transformer-based models, pretrained time series foundation models, and LLM-based forecasting approaches. Across tasks, we demonstrate that a mixture-of-experts model that fuses multiple pretrained forecasters achieves the strongest overall performance, indicating that heterogeneous pretrained representations provide complementary predictive information. Our results further show that numerical transformer-based models produce reliable forecasts, while pretraining provides the largest gains at longer horizons, particularly when the pretraining domain is mechanistically aligned with influenza dynamics. In contrast, LLM-based time series methods underperform relative to numerical forecasters in this setting. Finally, we examine hospitalization information as both an auxiliary covariate and a pretraining source. Hospitalization signals provide complementary improvements in selected settings and clarify when additional surveillance streams enhance the robustness of multi-horizon forecasting. These findings provide actionable guidance on model selection, pretraining strategy, and auxiliary-signal use for influenza preparedness.

• The paper demonstrates that a mixture-of-experts model achieves the lowest MSE (0.382) and highest NNSE (0.864) in 1-4 week influenza forecasting.
• Pretraining on mechanistically aligned data, such as M4 and hospitalization records, enhances forecast robustness, especially at 3-4 week horizons.
• LLM-based TSFMs underperform due to token-centric processing, emphasizing the need for domain-specific numerical architectures and auxiliary signals.

Systematic Evaluation of Time Series Foundation Models for Influenza Forecasting

Introduction

The quantitative forecasting of epidemic time series, particularly for seasonal influenza, remains a critical public health challenge, directly impacting intervention strategies, resource management, and surveillance. "Understanding Key Features of Time Series Foundation Models from Epidemic Forecasting" (2606.19560) provides a methodologically rigorous comparison of classical, neural, and foundation-style architectures for forecasting influenza-like illness (ILI) and influenza-associated hospitalization time series. The work operationalizes realistic multi-horizon (1-4-week-ahead) forecasting, adhering to CDC FluSight standards, across both temporal (within-region) and spatial (cross-region) generalization regimes. The core focus is the behavior, transferability, and integration of pretrained time series foundation models (TSFMs), with critical scrutiny of recent transformer/LLM-based advances.

Methodological Framework

A distinguishing characteristic of this study is the explicit separation of evaluation targets (ILI, hospitalizations) from auxiliary pretraining sources (M4, TrafficL, COVID-19 death data), rigorous prevention of data leakage, and harmonization with CDC reporting protocols. Two primary axes are considered:

• Temporal Generalization: Chronologically split within each HHS region, capturing operational forward-in-time forecasting.
• Spatial Generalization: Held-out regions test backbone transfer across geospatial and demographic distribution shift.

Seventeen neural and statistical baselines are systematically compared, spanning ARIMA, LSTM, TCN, TFT, TimesNet, PatchTST, iTransformer, TimeLLM, Chronos, and the authors’ mixture-of-experts MultiFoundationCore (MFC). Critical architectural distinctions include direct vs. iterative multi-horizon forecasts and the ability to natively utilize auxiliary signals.

Main Experimental Findings

Temporal (Within-Region) Forecasting

• Best Overall Model: The mixture-of-experts MultiFoundationCore, fusing multiple pretrained and pattern forecasters, consistently achieves the lowest MSE (0.382) and highest NNSE (0.864) in the main ILI benchmark, outperforming all individual models.
• Pretraining Gains: PatchTST and iTransformer display substantial improvements from cross-domain and especially mechanistically related pretraining. Gains are most pronounced at longer (3-4 week) forecast horizons. Pretraining on the M4 generic corpus (0.415 MSE, 0.856 NNSE) narrows the short-term gap but pretraining on aligned hospitalization data confers highest robustness.
• LLM-Based Methods: Foundation models using LLM-style tokenization and pretraining (Chronos, TimeLLM) underperform numerical transformers in these realistic 1-4-week tasks despite strong results reported elsewhere. The weakness is amplified at longer leads, and is attributed to inductive bias mismatch: token-centric processing degrades preservation of local dynamics, amplitudes, and mechanistic signals.
• Forecasting Strategy: Direct multi-output architectures dominate iterative roll-forward approaches, particularly at multi-step horizons, due to containment of error propagation.

Spatial (Cross-Region) Generalization

• Numeric Transformers Robust Across Regions: PatchTST is the top-performing model (MSE: 0.449, NNSE: 0.848) under spatial splits, followed closely by TFT and LSTM. All models exhibit elevated error compared to within-region splits, indicating nontrivial challenges in distributional transfer.
• LLM Foundation Models: Chronos is competitive for 1-week-ahead, but the advantage vanishes at multi-step horizons and for less densely pretrained settings.

Hospitalization Forecasting and Bidirectional Signal Utility

• Compact Models in Data-Scarce Regimes: With only three years of hospitalization data, regularized recurrent baselines (TinyLSTM) outperform high-capacity foundation models. Incorporation of ILI as an auxiliary input improves medium-range predictions across nearly all architectures.
• Bidirectional Transfer: Both as a pretraining source and as an exogenous covariate, ILI and hospitalization data provide significant mutual gains, especially at weeks 3-4, reinforcing the practical value of mechanistically linked multivariate modeling.

Practical Insights and Model Selection Guidelines

• Pretraining Domain Alignment: The efficacy of foundation models is maximized when pretraining and target domains are mechanistically connected (e.g., ILI ↔ hospitalization). Benchmarks relying solely on generic pretraining (e.g., M4, TrafficL) may overstate cross-domain transferability when deployed in public health.
• Auxiliary Signals: Architectures able to natively ingest multi-stream exogenous covariates (e.g., MFC, TFT, PatchTST with input stream) deliver robustness and adaptability in operational settings.
• Temporal Adaptation Frequency: Frequent retraining (down to every 10 windows) brings diminishing but nontrivial gains, especially at longer horizons, balancing computational and statistical efficacy.

Contradictory or Revised Claims

The study directly challenges prior claims that LLM reprogramming or general-purpose foundation models surpass numerical architectures in operational epidemic forecasting settings. Particularly, TimeLLM’s reported superior performance collapses under CDC-aligned 1-4 week horizons and multi-region stratification (2606.19560).

Implications and Future Directions

Theoretical

• Inductive Biases: The work highlights the necessity of model designs and pretraining methodologies that encode domain-appropriate inductive biases for continuous, mechanistic, and seasonal phenomena over tokenized, text-centric processing.
• Mixture-of-Experts Paradigm: The multi-architecture fusion approach (MFC) provides a stable means of integrating heterogeneous pretrained embeddings and auxiliary signals, outperforming any homogeneous backbone under real-world conditions.

Practical

• Model Selection for Public Health: Decision-makers should prioritize numerically oriented TSFMs, favor contextually pretraining on mechanistically linked surveillance streams, and exploit architectures supporting exogenous signals for maximal medium-range epidemic forecast stability.
• Benchmarking Best Practices: Proper regional stratification, harmonized preprocessing, and restriction to operational window lengths (1-4 weeks) are essential for reliable, deployable model evaluation in epidemic scenarios.

Outlook

The open release of standardized code, data splits, and pretrained checkpoints provides a foundation for reproducible benchmarking and innovation in TSFM research for public health. Priorities for further research include probabilistic extensions (uncertainty quantification, calibration), integration of mechanistic/causal modules into hybrid backbones, and extending analysis to broader epidemiological and environmental settings.

Conclusion

This comprehensive study establishes that, within the domain of epidemic time series forecasting, mixture-of-experts foundation models built on numerically specialized transformers—especially when enriched by mechanistically aligned pretraining and auxiliary signals—are superior to LLM-reprogrammed or language-centric TSFMs under operationally realistic settings. These findings inform both the theoretical development of time series foundation models and the practical deployment of forecasting systems critical to public health planning and resource allocation (2606.19560).