# RobustTSF: Towards Theory and Design of Robust Time Series Forecasting with Anomalies

arXiv: https://arxiv.org/abs/2402.02032 · HTML: https://mlsanity.com/paper/2402.02032/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 48 references that are in the map.
- First posted on arXiv 3 Feb 2024.

## Builds on (most cited first, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labels](https://mlsanity.com/paper/1712.05055/) (2017)
- [Learning from Noisy Labels with Deep Neural Networks: A Survey](https://mlsanity.com/paper/2007.08199/) (2020)
- [Learning under Concept Drift: A Review](https://mlsanity.com/paper/2004.05785/) (2020)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Robust Loss Functions under Label Noise for Deep Neural Networks](https://mlsanity.com/paper/1712.09482/) (2017)
- [Normalized Loss Functions for Deep Learning with Noisy Labels](https://mlsanity.com/paper/2006.13554/) (2020)
- [A review on outlier/anomaly detection in time series data](https://mlsanity.com/paper/2002.04236/) (2020)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [Learning with Instance-Dependent Label Noise: A Sample Sieve Approach](https://mlsanity.com/paper/2010.02347/) (2020)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Peer Loss Functions: Learning from Noisy Labels without Knowing Noise Rates](https://mlsanity.com/paper/1910.03231/) (2019)
- [A Second-Order Approach to Learning with Instance-Dependent Label Noise](https://mlsanity.com/paper/2012.11854/) (2020)
- [Clusterability as an Alternative to Anchor Points When Learning with Noisy Labels](https://mlsanity.com/paper/2102.05291/) (2021)
- [Robust regression with covariate filtering: Heavy tails and adversarial contamination](https://mlsanity.com/paper/2009.12976/) (2020)
- [Dynamic Gaussian Mixture based Deep Generative Model For Robust Forecasting on Sparse Multivariate Time Series](https://mlsanity.com/paper/2103.02164/) (2021)
- [Understanding Instance-Level Label Noise: Disparate Impacts and Treatments](https://mlsanity.com/paper/2102.05336/) (2021)
- [Robust Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2202.11910/) (2022)
- [Self-Adaptive Forecasting for Improved Deep Learning on Non-Stationary Time-Series](https://mlsanity.com/paper/2202.02403/) (2022)

## Built on by (most cited first, 18 of 18)

- [Rethinking the Power of Timestamps for Robust Time Series Forecasting: A Global-Local Fusion Perspective](https://mlsanity.com/paper/2409.18696/) (2024)
- [Kairos: Toward Adaptive and Parameter-Efficient Time Series Foundation Models](https://mlsanity.com/paper/2509.25826/) (2025)
- [Revisiting LLMs as Zero-Shot Time-Series Forecasters: Small Noise Can Break Large Models](https://mlsanity.com/paper/2506.00457/) (2025)
- [Modeling Temporal Dependencies within the Target for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2406.04777/) (2024)
- [Task-oriented Time Series Imputation Evaluation via Generalized Representers](https://mlsanity.com/paper/2410.06652/) (2024)
- [Diversified Scaling Inference in Time Series Foundation Models](https://mlsanity.com/paper/2601.17376/) (2026)
- [DropoutTS: Sample-Adaptive Dropout for Robust Time Series Forecasting](https://mlsanity.com/paper/2601.21726/) (2026)
- [Investigating a Model-Agnostic and Imputation-Free Approach for Irregularly-Sampled Multivariate Time-Series Modeling](https://mlsanity.com/paper/2502.15785/) (2025)
- [Quantifying Robustness: A Benchmarking Framework for Deep Learning Forecasting in Cyber-Physical Systems](https://mlsanity.com/paper/2504.03494/) (2025)
- [CoIFNet: A Unified Framework for Multivariate Time Series Forecasting with Missing Values](https://mlsanity.com/paper/2506.13064/) (2025)
- [SEER: Transformer-based Robust Time Series Forecasting via Automated Patch Enhancement and Replacement](https://mlsanity.com/paper/2602.00589/) (2026)
- [Contrastive Time Series Forecasting with Anomalies](https://mlsanity.com/paper/2512.11526/) (2025)
- [Policy-Controlled Generalized Share: A General Framework with a Transformer Instantiation for Strictly Online Switching-Oracle Tracking](https://mlsanity.com/paper/2603.28198/) (2026)
- [MorphStrata: Layer-Specific Perturbations for Generating Morphence Students in Time-Series Moving Target Defense](https://mlsanity.com/paper/2606.17435/) (2026)
- [TS-Fault: Benchmarking Time Series Forecasters Against Structural Faults](https://mlsanity.com/paper/2606.18539/) (2026)
- [DrafTS: Time-Aware Decomposition with Residual Correction for Time Series Modeling](https://mlsanity.com/paper/2609.33368/) (2026)
- [Towards Robust Time Series Learning via Capacity-Centric Modulation](https://mlsanity.com/paper/2609.39489/) (2026)
- [Time Series Forecasting Benchmarks Need Scenario-Grounded Stress Testing](https://mlsanity.com/paper/2610.02608/) (2026)

## Abstract (arXiv)

Time series forecasting is an important and forefront task in many real-world applications. However, most of time series forecasting techniques assume that the training data is clean without anomalies. This assumption is unrealistic since the collected time series data can be contaminated in practice. The forecasting model will be inferior if it is directly trained by time series with anomalies. Thus it is essential to develop methods to automatically learn a robust forecasting model from the contaminated data. In this paper, we first statistically define three types of anomalies, then theoretically and experimentally analyze the loss robustness and sample robustness when these anomalies exist. Based on our analyses, we propose a simple and efficient algorithm to learn a robust forecasting model. Extensive experiments show that our method is highly robust and outperforms all existing approaches. The code is available at https://github.com/haochenglouis/RobustTSF.