Sustainability of TSFM Deployment and Pretraining: From Carbon Footprint Analysis to Mitigation via Pruning

Time series foundation models (TSFMs) have emerged as general-purpose models for time series analysis, but pretraining alone is often insufficient for reliable downstream deployment. Bridging this gap requires further intervention to handle domain shift, task heterogeneity, limited supervision, and computational constraints, which motivates post-training as a broad class of methods to adapt, augment, compose, calibrate, or specialize pretrained TSFMs for downstream tasks. In this work, we analyze TSFM post-training methods based on their locus of intervention in the prediction pipeline, yielding five categories: parameter adaptation, context augmentation, model composition, output processing and uncertainty control, and compression and specialization. Within each category, we study main representative methods and discuss their current limitations. We further identify future directions toward controlled adaptation, reliable context construction, uncertainty-aware model composition, calibrated output processing, and deployment-aware specialization. Overall, by providing a unifying framework for the emerging TSFM post-training landscape, this work aims to support future research to navigate the design space between a pretrained TSFM and its reliable downstream deployment.

While Time Series Foundation Models (TSFMs) excel in zero-shot tasks, their behavior under continual fine tuning is poorly understood. We present the first systematic study of catastrophic forgetting in TSFMs (TimesFM-2.0, Chronos-2) versus a specialized SamFormer model across synthetic and real-world energy forecasting benchmarks. Our results show that while fine-tuning improves new task accuracy, it consistently triggers forgetting, though larger models exhibit greater inherent robustness. Notably, employing forgetting mitigation techniques such as DER, levels the playing field: it provides disproportionate gains to smaller models, allowing them to match TSFM performance by the end of the continual learning sequence. These findings suggest that in realistic, non-stationary scenarios, the high computational cost of large foundation models may not be justified over smaller models equipped with effective mitigation strategies.

Deploying a time series foundation model requires GPU infrastructure, engineering overhead, and carries no guarantee of improvement over XGBoost. We provide the first systematic break-even analysis answering when this investment pays off. Across 30 benchmark datasets, we compare zero-shot and LoRA fine-tuned foundation models (Chronos, Moirai, Lag-Llama) against classical baselines (Naive, ETS, ARIMA, XGBoost) at six training set sizes from 2% to 100% of available data. Foundation models outperform classical methods at every evaluated training fraction on 15 of 30 datasets -- GPU deployment is unconditionally justified on these regardless of data volume. On 6 datasets, classical methods surpass zero-shot foundation models with as little as 2% of training data (21-2,768 samples); on the remaining 9, break-even ranges from 24 to 8,361 samples. One robust deployment rule requires no model training: if n_train < 700 and seasonality is non-negligible, use FM zero-shot and skip fine-tuning -- this resolves 10 of 30 deployment decisions immediately. Contrary to common practice, LoRA fine-tuning can actively degrade performance on short series. We operationalise these findings as a two-step decision framework -- compute dataset length and seasonality strength, run a brief 5-10% pilot only if needed -- enabling practitioners to make the FM-versus-classical decision before committing to full infrastructure. Four dataset features motivate mechanistic hypotheses for the remaining cases, though reliable automated prediction at this benchmark scale remains an open problem. Code, benchmark, and decision tools are available at https://github.com/nicolaisi/fm-breakeven.