Organizations: School of Artificial Intelligence and Robotics, Xiamen University Malaysia · S.M.A.R.T. NEXUS Centre of Excellence, Xiamen University Malaysia Sepang, Selangor 43900, Malaysia
Abstract
Test-Time Adaptation (TTA) aims to improve time series forecasting under distribution shifts by using limited observations revealed during inference. However, forecasting TTA must operate in a source-free online setting, where the adaptation signal is short, temporally correlated, and potentially noisy. Existing methods can therefore suffer from weak identifiability, error accumulation, and unstable long-horizon corrections when the revealed prefix is sparse or contaminated. To address these issues, we propose STEPS, a Smooth Temporal Error Propagation Solver for TTA in time-series forecasting. STEPS reformulates forecasting TTA as a Dirichlet Boundary Value Problem on a temporal manifold, where the revealed prefix error serves as the boundary condition for the unknown future error field. Then, STEPS solves a smooth and bounded correction field in prediction space: a Local Solver propagates prefix errors under temporal smoothness, a Global Solver retrieves stable cross-window error memory and Spatiotemporal Manifold Fusion (SMF) integrates both solutions into the final correction. Across six standard benchmarks and four frozen backbones, STEPS achieves an average relative MSE reduction of 26.82% over the zero-shot backbone, exceeding the strongest compared TTA baseline by 12.77%. Additional sparse prefix and contamination tests confirm the robustness of STEPS under limited and noisy prefixes.
Test-time adaptation (TTA) has recently emerged as a promising approach for improving time series forecasting (TSF) under distribution shift. Existing TSF-TTA methods differ in how they utilize revealed targets, yet the resulting adaptation protocols remain heterogeneous and lack a clearly unified formulation. To address this issue, we revisit TSF-TTA from the perspective of protocol cleanliness and propose an adaptation protocol based solely on matured ground truth, yielding a more principled setting for adaptation. Under this protocol, we further diagnose existing adapters in the frequency domain and find that their prediction corrections often exhibit limited and weakly structured spectral modifications. Motivated by this diagnosis, we propose Frequency-Aware Calibration (FAC), a lightweight calibration method that directly parameterizes prediction corrections in the frequency domain. Across diverse datasets, forecasting horizons, and source forecasters, FAC achieves competitive and consistent performance while requiring substantially fewer trainable parameters than the compared TSF-TTA adapters.
Time Series Foundation Models (TSFMs) advance generalization and data efficiency in time series forecasting by unified large-scale pretraining. But TSFMs remain lacking when adapting to specific downstream forecasting tasks for two reasons. First, the non-stationary and uncertain nature of time series data lead to inevitable temporal distribution shifts between historical training and future testing data, while current Supervised FineTuning (SFT)-based methods are prone to overfitting and may degrade generalization. Second, training data availability varies across forecasting tasks, requiring TSFMs to generalize well under diverse data regimes. To address these challenges, we introduce the Time series Reinforcement Finetuning (TimeRFT) paradigm for TSFM downstream adaptation, which consists of two task-specific training recipes: i) A forecasting quality-based temporal reward mechanism that conducts a multi-faceted evaluation of the contribution of each prediction step to overall forecasting accuracy. ii) A forecasting difficulty-based data selection strategy to identify time series samples with generalizable predictive patterns and informative training signals. Extensive experiments demonstrate TimeRFT can consistently outperform SFT-based adaptation methods across various real-world forecasting tasks and training data regimes, enhancing prediction accuracy and generalization against unforeseen distribution shifts.
Large \emph{Time Series Foundation Models} (TSFMs) demonstrate strong zero-shot forecasting capabilities across diverse domains. However, their application to regional climate forecasting faces practical challenges: model weights are often proprietary, local training records are limited, and computational budgets are constrained, making traditional fine-tuning approaches infeasible. To address these constraints, we introduce a lightweight, black-box adaptation framework (requiring no access to backbone parameters and no backbone fine-tuning) that enhances frozen TSFMs at inference time through two plug-and-play wrappers: \textbf{SMR\textsuperscript{2}} (Stationarity aware multi-resolution Residual), which decomposes the input into multi-resolution temporal views, learns stride specific residual corrections that capture regional dynamics, then adaptively ensembles them into a single forecast, and \textbf{MBB} (Moving Block Bootstrap), which preserves temporal dependencies through block resampling and ensembles over temporally coherent residual perturbations to stabilize the point forecast. Both wrappers instantiate the same bagging style principle: they build diverse views of the input or its residuals, forecast each with the same frozen backbone, and aggregate, so all adaptation comes from inference time ensembling rather than any weight update. Evaluated on one month ahead Standardized Precipitation Evapotranspiration Index (SPEI) prediction across multiple sites in South Australia, our framework consistently improves forecasting performance across several backbone models, demonstrating up to 26% mean squared error (MSE) reduction over the corresponding frozen backbone while enabling practical deployment in resource constrained regional forecasting systems.