# Online time series prediction using feature adjustment

arXiv: https://arxiv.org/abs/2509.03810 · HTML: https://mlsanity.com/paper/2509.03810/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 51 references that are in the map.
- First posted on arXiv 4 Sep 2025.

## Builds on (most cited first, 30 of 37)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Domain Randomization for Transferring Deep Neural Networks from Simulation to the Real World](https://mlsanity.com/paper/1703.06907/) (2017)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [End-to-End Incremental Learning](https://mlsanity.com/paper/1807.09536/) (2018)
- [Continual Test-Time Domain Adaptation](https://mlsanity.com/paper/2203.13591/) (2022)
- [Domain Generalization via Model-Agnostic Learning of Semantic Features](https://mlsanity.com/paper/1910.13580/) (2019)
- [MEMO: Test Time Robustness via Adaptation and Augmentation](https://mlsanity.com/paper/2110.09506/) (2021)
- [Learning to Learn Single Domain Generalization](https://mlsanity.com/paper/2003.13216/) (2020)
- [Robust Test-Time Adaptation in Dynamic Scenarios](https://mlsanity.com/paper/2303.13899/) (2023)
- [Uncertainty-based Continual Learning with Adaptive Regularization](https://mlsanity.com/paper/1905.11614/) (2019)
- [Dish-TS: A General Paradigm for Alleviating Distribution Shift in Time Series Forecasting](https://mlsanity.com/paper/2302.14829/) (2023)
- [Best sources forward: domain generalization through source-specific nets](https://mlsanity.com/paper/1806.05810/) (2018)
- [SOFTS: Efficient Multivariate Time Series Forecasting with Series-Core Fusion](https://mlsanity.com/paper/2404.14197/) (2024)
- [Time Series Prediction using Deep Learning Methods in Healthcare](https://mlsanity.com/paper/2108.13461/) (2021)
- [OneNet: Enhancing Time Series Forecasting Models under Concept Drift by Online Ensembling](https://mlsanity.com/paper/2309.12659/) (2023)
- [Few-Shot Class-Incremental Learning via Entropy-Regularized Data-Free Replay](https://mlsanity.com/paper/2207.11213/) (2022)
- [Tracking Slowly Moving Clairvoyant: Optimal Dynamic Regret of Online Learning with True and Noisy Gradient](https://mlsanity.com/paper/1605.04638/) (2016)
- [Continual Learning via Local Module Composition](https://mlsanity.com/paper/2111.07736/) (2021)
- [A Unified Feature Disentangler for Multi-Domain Image Translation and Manipulation](https://mlsanity.com/paper/1809.01361/) (2018)
- [ViDA: Homeostatic Visual Domain Adapter for Continual Test Time Adaptation](https://mlsanity.com/paper/2306.04344/) (2023)
- [Model Zoo: A Growing "Brain" That Learns Continually](https://mlsanity.com/paper/2106.03027/) (2021)
- [Frequency Adaptive Normalization For Non-stationary Time Series Forecasting](https://mlsanity.com/paper/2409.20371/) (2024)
- [Learning Fast and Slow for Online Time Series Forecasting](https://mlsanity.com/paper/2202.11672/) (2022)
- [Battling the Non-stationarity in Time Series Forecasting via Test-time Adaptation](https://mlsanity.com/paper/2501.04970/) (2025)
- [Predictive Inference with Feature Conformal Prediction](https://mlsanity.com/paper/2210.00173/) (2022)

## Built on by (most cited first, 4 of 4)

- [Learning the Context of Errors: Black-Box Online Adaptation of Time Series Foundation Models](https://mlsanity.com/paper/2606.14222/) (2026)
- [Towards Principled Test-Time Adaptation for Time Series Forecasting](https://mlsanity.com/paper/2605.17250/) (2026)
- [TEFL: Prediction-Residual-Guided Rolling Forecasting for Multi-Horizon Time Series](https://mlsanity.com/paper/2602.22520/) (2026)
- [Adapt Only When It Pays: Budgeted Decision-Loss Priority for Delayed Online Time-Series Adaptation](https://mlsanity.com/paper/2606.25068/) (2026)

## Abstract (arXiv)

Time series forecasting is of significant importance across various domains. However, it faces significant challenges due to distribution shift. This issue becomes particularly pronounced in online deployment scenarios where data arrives sequentially, requiring models to adapt continually to evolving patterns. Current time series online learning methods focus on two main aspects: selecting suitable parameters to update (e.g., final layer weights or adapter modules) and devising suitable update strategies (e.g., using recent batches, replay buffers, or averaged gradients). We challenge the conventional parameter selection approach, proposing that distribution shifts stem from changes in underlying latent factors influencing the data. Consequently, updating the feature representations of these latent factors may be more effective. To address the critical problem of delayed feedback in multi-step forecasting (where true values arrive much later than predictions), we introduce ADAPT-Z (Automatic Delta Adjustment via Persistent Tracking in Z-space). ADAPT-Z utilizes an adapter module that leverages current feature representations combined with historical gradient information to enable robust parameter updates despite the delay. Extensive experiments demonstrate that our method consistently outperforms standard base models without adaptation and surpasses state-of-the-art online learning approaches across multiple datasets.