Time series forecasting plays a vital role in various real-world applications and has attracted significant attention in recent decades. While recent methods have achieved remarkable accuracy by incorporating advanced inductive biases and training strategies, we observe that instance-level variations remain a significant challenge. These variations--stemming from distribution shifts, missing data, and long-tail patterns--often lead to suboptimal forecasts for specific instances, even when overall performance appears strong. To address this issue, we propose a model-agnostic framework, PIR, designed to enhance forecasting performance through Post-forecasting Identification and Revision. Specifically, PIR first identifies biased forecasting instances by estimating their accuracy. Based on this, the framework revises the forecasts using contextual information, including covariates and historical time series, from both local and global perspectives in a post-processing fashion. Extensive experiments on real-world datasets with mainstream forecasting models demonstrate that PIR effectively mitigates instance-level errors and significantly improves forecasting reliability.

Time series forecasting is crucial for applications across multiple domains and various scenarios. Although Transformers have dramatically advanced the landscape of forecasting, their effectiveness remains debated.

B.4 Existing theoretical intuition and empirical comparison to the proposed OCP block.

Correlation mechanism to capture cross-time dependency for forecasting. Besides, the dimension of the channel is set to 16 based on efficiency considerations. Weather, and the look-back window size is set as 96. Proposition 2. The time and space complexity for the Cross-variable GNN is Frequency enhanced decomposed transformer for long-term series forecasting.

Recent adaptations of Large Language Models (LLMs) for time series forecasting often fail to effectively enhance information for raw series, leaving LLM reasoning capabilities underutilized. Existing prompting strategies rely on static correlations rather than generative interpretations of dynamic behavior, lacking critical global and instance-specific context. To address this, we propose STELLA (Semantic-Temporal Alignment with Language Abstractions), a framework that systematically mines and injects structured supplementary and complementary information. STELLA employs a dynamic semantic abstraction mechanism that decouples input series into trend, seasonality, and residual components. It then translates intrinsic behavioral features of these components into Hierarchical Semantic Anchors: a Corpus-level Semantic Prior (CSP) for global context and a Fine-grained Behavioral Prompt (FBP) for instance-level patterns. Using these anchors as prefix-prompts, STELLA guides the LLM to model intrinsic dynamics. Experiments on eight benchmark datasets demonstrate that STELLA outperforms state-of-the-art methods in long- and short-term forecasting, showing superior generalization in zero-shot and few-shot settings. Ablation studies further validate the effectiveness of our dynamically generated semantic anchors.

Small Earth data are geoscience observations with limited short-term monitoring variability, providing sparse but meaningful measurements, typically exhibiting spatiotemporal correlations. Spatiotemporal forecasting on such data is crucial for understanding geoscientific processes despite their small scale. However, conventional deep learning models for spatiotemporal forecasting requires task-specific training for different scenarios. Foundation models do not need task-specific training, but they often exhibit forecasting bias toward the global mean of the pretraining distribution. Here we propose a simple and robust approach for spatiotemporally correlated small Earth data forecasting. The essential idea is to characterize and quantify spatiotemporal patterns of small Earth data and then utilize tabular foundation models for accurate forecasting across different scenarios. Comparative results across three typical scenarios demonstrate that our forecasting approach achieves superior accuracy compared to the graph deep learning model (T -GCN) and tabular foundation model (TabPFN) in the majority of instances, exhibiting stronger robustness. Keywords: Small Earth data, Spatiotemporal correlations, Tabular foundation model, Forecasting, Deep learning 1. Introduction Small Earth data refers to geoscience time-series observations in which short-term monitoring provides limited informative variation, resulting in only sparse but meaningful measurements being available. These data predominantly possess spatiotemporal correlations. Despite their small scale, forecasting on such data is of critical importance for understanding geoscientific processes (Saad et al., 2024; Y u et al., 2024).

Time series forecasting is crucial for applications across multiple domains and various scenarios. Although Transformers have dramatically advanced the landscape of forecasting, their effectiveness remains debated.