# Robust Multivariate Time-Series Forecasting: Adversarial Attacks and Defense Mechanisms

arXiv: https://arxiv.org/abs/2207.09572 · HTML: https://mlsanity.com/paper/2207.09572/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 45 references that are in the map.
- First posted on arXiv 19 Jul 2022.

## Builds on (most cited first, 25 of 25)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Adversarial Attack on Graph Structured Data](https://mlsanity.com/paper/1806.02371/) (2018)
- [Towards Fast Computation of Certified Robustness for ReLU Networks](https://mlsanity.com/paper/1804.09699/) (2018)
- [Time Series Data Augmentation for Deep Learning: A Survey](https://mlsanity.com/paper/2002.12478/) (2020)
- [Certified Adversarial Robustness with Additive Noise](https://mlsanity.com/paper/1809.03113/) (2018)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Sparse and Imperceivable Adversarial Attacks](https://mlsanity.com/paper/1909.05040/) (2019)
- [Deep Factors for Forecasting](https://mlsanity.com/paper/1905.12417/) (2019)
- [Network Inference via the Time-Varying Graphical Lasso](https://mlsanity.com/paper/1703.01958/) (2017)
- [Learning Quantile Functions without Quantile Crossing for Distribution-free Time Series Forecasting](https://mlsanity.com/paper/2111.06581/) (2021)
- [Adversarial Examples in Deep Learning for Multivariate Time Series Regression](https://mlsanity.com/paper/2009.11911/) (2020)
- [Multivariate Quantile Function Forecaster](https://mlsanity.com/paper/2202.11316/) (2022)
- [Robust Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2202.11910/) (2022)
- [A Word is Worth A Thousand Dollars: Adversarial Attack on Tweets Fools Stock Predictions](https://mlsanity.com/paper/2205.01094/) (2022)
- [Recurrent Neural Filters: Learning Independent Bayesian Filtering Steps for Time Series Prediction](https://mlsanity.com/paper/1901.08096/) (2019)
- [Adversarial Attacks on Probabilistic Autoregressive Forecasting Models](https://mlsanity.com/paper/2003.03778/) (2020)
- [Adversarial Attacks on Multivariate Time Series](https://mlsanity.com/paper/2004.00410/) (2020)
- [Structured Policy Iteration for Linear Quadratic Regulator](https://mlsanity.com/paper/2007.06202/) (2020)

## Built on by (most cited first, 8 of 8)

- [Self-Supervised Learning for Time Series Analysis: Taxonomy, Progress, and Prospects](https://mlsanity.com/paper/2306.10125/) (2023)
- [A Survey on Time-Series Pre-Trained Models](https://mlsanity.com/paper/2305.10716/) (2023)
- [Adversarial Vulnerabilities in Large Language Models for Time Series Forecasting](https://mlsanity.com/paper/2412.08099/) (2024)
- [Trojan Horse Hunt in Time Series Forecasting for Space Operations](https://mlsanity.com/paper/2506.01849/) (2025)
- [Breaking Boundaries: Balancing Performance and Robustness in Deep Wireless Traffic Forecasting](https://mlsanity.com/paper/2311.09790/) (2023)
- [Boosting Certified Robustness for Time Series Classification with Efficient Self-Ensemble](https://mlsanity.com/paper/2409.02802/) (2024)
- [Exposing Vulnerabilities in Explanation for Time Series Classifiers via Dual-Target Attacks](https://mlsanity.com/paper/2602.02763/) (2026)
- [LogiC-Diff: Embedding Security Properties Into AI-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2609.38381/) (2026)

## Abstract (arXiv)

This work studies the threats of adversarial attack on multivariate probabilistic forecasting models and viable defense mechanisms. Our studies discover a new attack pattern that negatively impact the forecasting of a target time series via making strategic, sparse (imperceptible) modifications to the past observations of a small number of other time series. To mitigate the impact of such attack, we have developed two defense strategies. First, we extend a previously developed randomized smoothing technique in classification to multivariate forecasting scenarios. Second, we develop an adversarial training algorithm that learns to create adversarial examples and at the same time optimizes the forecasting model to improve its robustness against such adversarial simulation. Extensive experiments on real-world datasets confirm that our attack schemes are powerful and our defense algorithms are more effective compared with baseline defense mechanisms.