# Calibration of Time-Series Forecasting: Detecting and Adapting Context-Driven Distribution Shift

arXiv: https://arxiv.org/abs/2310.14838 · HTML: https://mlsanity.com/paper/2310.14838/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 34 references that are in the map.
- First posted on arXiv 23 Oct 2023.

## Builds on (most cited first, 9 of 9)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Failing Loudly: An Empirical Study of Methods for Detecting Dataset Shift](https://mlsanity.com/paper/1810.11953/) (2018)
- [AdaRNN: Adaptive Learning and Forecasting of Time Series](https://mlsanity.com/paper/2108.04443/) (2021)
- [Dish-TS: A General Paradigm for Alleviating Distribution Shift in Time Series Forecasting](https://mlsanity.com/paper/2302.14829/) (2023)
- [Feature Shift Detection: Localizing Which Features Have Shifted via Conditional Distribution Tests](https://mlsanity.com/paper/2107.06929/) (2021)

## Built on by (most cited first, 25 of 25)

- [VisionTS: Visual Masked Autoencoders Are Free-Lunch Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2408.17253/) (2024)
- [Proactive Model Adaptation Against Concept Drift for Online Time Series Forecasting](https://mlsanity.com/paper/2412.08435/) (2024)
- [Out-of-Distribution Generalization in Time Series: A Survey](https://mlsanity.com/paper/2503.13868/) (2025)
- [The Forecast After the Forecast: A Post-Processing Shift in Time Series](https://mlsanity.com/paper/2601.20280/) (2026)
- [Learning the Context of Errors: Black-Box Online Adaptation of Time Series Foundation Models](https://mlsanity.com/paper/2606.14222/) (2026)
- [Selective Learning for Deep Time Series Forecasting](https://mlsanity.com/paper/2510.25207/) (2025)
- [Online time series prediction using feature adjustment](https://mlsanity.com/paper/2509.03810/) (2025)
- [Embracing Large Language Models in Traffic Flow Forecasting](https://mlsanity.com/paper/2412.12201/) (2024)
- [Bridging Distribution Gaps in Time Series Foundation Model Pretraining with Prototype-Guided Normalization](https://mlsanity.com/paper/2504.10900/) (2025)
- [PromptTSS: A Prompting-Based Approach for Interactive Multi-Granularity Time Series Segmentation](https://mlsanity.com/paper/2506.11170/) (2025)
- [MetaEformer: Unveiling and Leveraging Meta-patterns for Complex and Dynamic Systems Load Forecasting](https://mlsanity.com/paper/2506.12800/) (2025)
- [Inner-Instance Normalization for Time Series Forecasting](https://mlsanity.com/paper/2510.08657/) (2025)
- [Learning from Yesterday's Error: An Efficient Online Learning Method for Traffic Demand Prediction](https://mlsanity.com/paper/2602.21757/) (2026)
- [Dynamic Multi-period Experts for Online Time Series Forecasting](https://mlsanity.com/paper/2603.09062/) (2026)
- [On-Device Adaptive Battery Power Prediction for Electric Vehicles](https://mlsanity.com/paper/2607.09400/) (2026)
- [CONTINA: Confidence Interval for Traffic Demand Prediction with Coverage Guarantee](https://mlsanity.com/paper/2504.13961/) (2025)
- [Perseus: Interactive Time Series Segmentation with Sparse Supervision via Stateful Memory](https://mlsanity.com/paper/2510.09930/) (2025)
- [ADAPTOOD: Uncertainty-Aware Fine-Tuning for Out-of-Distribution ECG Time Series Models](https://mlsanity.com/paper/2606.04164/) (2026)
- [Public transit gains and spatially uneven travel demand changes after NYC congestion pricing](https://mlsanity.com/paper/2606.17530/) (2026)
- [When Does Online Adaptation Pay on the Edge? A Leakage-Free Evaluation of Warmup, Learning-Rate Selection, and Resource Trade-offs for Time-Series Forecasting](https://mlsanity.com/paper/2609.01126/) (2026)
- [Downside-Controlled Online Forecast Combination under Delayed and Revised Outcomes](https://mlsanity.com/paper/2609.29096/) (2026)
- [EPOC: Endpoint-Preserving Online Correction With Compressed Residual State for Multi-Horizon Time Series Forecasting](https://mlsanity.com/paper/2609.30929/) (2026)
- [Model-Agnostic Online Certificate-Driven Calibration for Time Series Forecasting Under Distribution Shift](https://mlsanity.com/paper/2609.31960/) (2026)
- [Correction-space Cross-variate Interaction for Test-time Adaptation in Time Series Forecasting](https://mlsanity.com/paper/2609.34638/) (2026)
- [ECHO: Correcting Time Series Foundation Model Forecasts with Historical Analogues and Errors](https://mlsanity.com/paper/2610.16433/) (2026)

## Abstract (arXiv)

Recent years have witnessed the success of introducing deep learning models to time series forecasting. From a data generation perspective, we illustrate that existing models are susceptible to distribution shifts driven by temporal contexts, whether observed or unobserved. Such context-driven distribution shift (CDS) introduces biases in predictions within specific contexts and poses challenges for conventional training paradigms. In this paper, we introduce a universal calibration methodology for the detection and adaptation of CDS with a trained model. To this end, we propose a novel CDS detector, termed the "residual-based CDS detector" or "Reconditionor", which quantifies the model's vulnerability to CDS by evaluating the mutual information between prediction residuals and their corresponding contexts. A high Reconditionor score indicates a severe susceptibility, thereby necessitating model adaptation. In this circumstance, we put forth a straightforward yet potent adapter framework for model calibration, termed the "sample-level contextualized adapter" or "SOLID". This framework involves the curation of a contextually similar dataset to the provided test sample and the subsequent fine-tuning of the model's prediction layer with a limited number of steps. Our theoretical analysis demonstrates that this adaptation strategy can achieve an optimal bias-variance trade-off. Notably, our proposed Reconditionor and SOLID are model-agnostic and readily adaptable to a wide range of models. Extensive experiments show that SOLID consistently enhances the performance of current forecasting models on real-world datasets, especially on cases with substantial CDS detected by the proposed Reconditionor, thus validating the effectiveness of the calibration approach.