# Online Learning for Time Series Prediction

arXiv: https://arxiv.org/abs/1302.6927 · HTML: https://mlsanity.com/paper/1302.6927/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2013.

## Built on by (most cited first, 30 of 33)

- [OneNet: Enhancing Time Series Forecasting Models under Concept Drift by Online Ensembling](https://mlsanity.com/paper/2309.12659/) (2023)
- [Learning Fast and Slow for Online Time Series Forecasting](https://mlsanity.com/paper/2202.11672/) (2022)
- [Online Learning with Simple Predictors and a Combinatorial Characterization of Minimax in 0/1 Games](https://mlsanity.com/paper/2102.01646/) (2021)
- [Online Dynamics Learning for Predictive Control with an Application to Aerial Robots](https://mlsanity.com/paper/2207.09344/) (2022)
- [Can Transformers Learn Optimal Filtering for Unknown Systems?](https://mlsanity.com/paper/2308.08536/) (2023)
- [Addressing Concept Shift in Online Time Series Forecasting: Detect-then-Adapt](https://mlsanity.com/paper/2403.14949/) (2024)
- [Unconstrained Dynamic Regret via Sparse Coding](https://mlsanity.com/paper/2301.13349/) (2023)
- [Stochastic Online Convex Optimization. Application to probabilistic time series forecasting](https://mlsanity.com/paper/2102.00729/) (2021)
- [Adversarially Robust PAC Learnability of Real-Valued Functions](https://mlsanity.com/paper/2206.12977/) (2022)
- [Act Now: A Novel Online Forecasting Framework for Large-Scale Streaming Data](https://mlsanity.com/paper/2412.00108/) (2024)
- [Universal Sequence Preconditioning](https://mlsanity.com/paper/2502.06545/) (2025)
- [Brain-Inspired Spiking Neural Network for Online Unsupervised Time Series Prediction](https://mlsanity.com/paper/2304.04697/) (2023)
- [Predictive Linear Online Tracking for Unknown Targets](https://mlsanity.com/paper/2402.10036/) (2024)
- [Universal Learning of Nonlinear Dynamics](https://mlsanity.com/paper/2508.11990/) (2025)
- [Research Program: Theory of Learning in Dynamical Systems](https://mlsanity.com/paper/2512.19410/) (2025)
- [Fairness in Forecasting of Observations of Linear Dynamical Systems](https://mlsanity.com/paper/2209.05274/) (2022)
- [Model-free Online Learning for the Kalman Filter: Forgetting Factor and Logarithmic Regret](https://mlsanity.com/paper/2505.08982/) (2025)
- [ONE-NAS: An Online NeuroEvolution based Neural Architecture Search for Time Series Forecasting](https://mlsanity.com/paper/2202.13471/) (2022)
- [Optimistic Optimisation of Composite Objective with Exponentiated Update](https://mlsanity.com/paper/2208.04065/) (2022)
- [Learning from time-dependent streaming data with online stochastic algorithms](https://mlsanity.com/paper/2205.12549/) (2022)
- [Online Evolutionary Neural Architecture Search for Multivariate Non-Stationary Time Series Forecasting](https://mlsanity.com/paper/2302.10347/) (2023)
- [Evolving Multi-Scale Normalization for Time Series Forecasting under Distribution Shifts](https://mlsanity.com/paper/2409.19718/) (2024)
- [Personalized Federated Learning for Cellular VR: Online Learning and Dynamic Caching](https://mlsanity.com/paper/2501.11745/) (2025)
- [Online Time Series Forecasting with Theoretical Guarantees](https://mlsanity.com/paper/2510.18281/) (2025)
- [POLA: Online Time Series Prediction by Adaptive Learning Rates](https://mlsanity.com/paper/2102.08907/) (2021)
- [The Complexity of Sequential Prediction in Dynamical Systems](https://mlsanity.com/paper/2402.06614/) (2024)
- [OML-AD: Online Machine Learning for Anomaly Detection in Time Series Data](https://mlsanity.com/paper/2409.09742/) (2024)
- [WAX-ML: A Python library for machine learning and feedback loops on streaming data](https://mlsanity.com/paper/2106.06524/) (2021)
- [Personalized Online Machine Learning](https://mlsanity.com/paper/2109.10452/) (2021)
- [Online estimation methods for irregular autoregressive models](https://mlsanity.com/paper/2302.10785/) (2023)

## Abstract (arXiv)

In this paper we address the problem of predicting a time series using the ARMA (autoregressive moving average) model, under minimal assumptions on the noise terms. Using regret minimization techniques, we develop effective online learning algorithms for the prediction problem, without assuming that the noise terms are Gaussian, identically distributed or even independent. Furthermore, we show that our algorithm's performances asymptotically approaches the performance of the best ARMA model in hindsight.