Long-term time series forecasting benefits from preserving global structure such as trends and seasonality. Recent LLM-based forecasters often improve accuracy through test-time scaling (e.g., iterative refinement), but these methods are computationally expensive and increasingly prone to global-shape mismatch as the prediction horizon extends. We propose SCALER, a coarse-to-fine forecasting framework that first employs a lightweight Transformer tailored to long-term shape modeling to predict a coarse representation of future dynamics. This predicted shape then serves as a compact guide for an LLM to perform test-time scaling via iterative coarse-to-fine residual token refinement, while processing substantially fewer tokens at each step. By guiding refinement with an explicit future-shape prediction, SCALER reduces reliance on long description prompts, and its fixed-step refinement avoids costly reward-model-based selection, further lowering computational overhead. Experimental results demonstrate that SCALER outperforms strong forecasting baselines in long-term, short-term and zero-shot forecasting while significantly reducing the inference cost associated with scaled LLM for time series forecasting. Code: https://github.com/xuanmay2701/SCALER.
Medical and public health experts must make real-time resource decisions, such as expanding hospital bed capacity, based on projected hospitalization trends during large-scale healthcare disruptions (e.g., operational failures or pandemics). Forecasting models can assist in this task by analyzing large volumes of resource-related data at the facility level, but they must be reliable for decision-making under real-world data conditions. Recent work shows that large language models (LLMs) can incorporate richer forms of context into numerical forecasting. Whereas traditional models rely primarily on temporal context (i.e., past observations), LLMs can also leverage non-temporal public health context such as demographic, geographic, and population-level features. However, it remains unclear how these models should be used to produce stable or decision-relevant predictions in real-world healthcare settings. To evaluate how LLMs can be effectively used in this setting, we evaluate three approaches across 60 counties with low-,mid-, and high-hospitalization intensities in the United States: direct LLM-based forecasting, classical time-series models, and a context-augmented hybrid pipeline (HybridARX) that incorporates LLM-derived signals into structured models. Because the goal is operational decision-making rather than error minimization alone, we evaluate performance with bias and lead-lag alignment in addition to standard forecasting metrics. Our results show that HybridARX improves over classical ARX by yielding more stable and better-calibrated forecasts, particularly when incorporating noisy contextual signals into structured time-series models. These findings suggest that, in non-stationary healthcare resource forecasting, LLMs are most useful when embedded within structured hybrid models.