# Counterfactual Explanation for Multivariate Time Series Forecasting with Exogenous Variables

arXiv: https://arxiv.org/abs/2511.06906 · HTML: https://mlsanity.com/paper/2511.06906/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 36 references that are in the map.
- First posted on arXiv 10 Nov 2025.

## Builds on (most cited first, 18 of 18)

- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Counterfactual Visual Explanations](https://mlsanity.com/paper/1904.07451/) (2019)
- [Techniques for Interpretable Machine Learning](https://mlsanity.com/paper/1808.00033/) (2018)
- [Explainable AI (XAI): A Systematic Meta-Survey of Current Challenges and Future Opportunities](https://mlsanity.com/paper/2111.06420/) (2021)
- [TimeSHAP: Explaining Recurrent Models through Sequence Perturbations](https://mlsanity.com/paper/2012.00073/) (2020)
- [Instance-based Counterfactual Explanations for Time Series Classification](https://mlsanity.com/paper/2009.13211/) (2020)
- [Counterfactual Explanations for Machine Learning on Multivariate Time Series Data](https://mlsanity.com/paper/2008.10781/) (2020)
- [Counterfactual Explanations in Sequential Decision Making Under Uncertainty](https://mlsanity.com/paper/2107.02776/) (2021)
- [A Survey on Graph Counterfactual Explanations: Definitions, Methods, Evaluation, and Research Challenges](https://mlsanity.com/paper/2210.12089/) (2022)
- [Text-to-Image Models for Counterfactual Explanations: a Black-Box Approach](https://mlsanity.com/paper/2309.07944/) (2023)
- [Self-Interpretable Time Series Prediction with Counterfactual Explanations](https://mlsanity.com/paper/2306.06024/) (2023)
- [Diverse Counterfactual Explanations for Anomaly Detection in Time Series](https://mlsanity.com/paper/2203.11103/) (2022)
- [Counterfactual Explanations for Time Series Forecasting](https://mlsanity.com/paper/2310.08137/) (2023)
- [M-CELS: Counterfactual Explanation for Multivariate Time Series Data Guided by Learned Saliency Maps](https://mlsanity.com/paper/2411.02649/) (2024)
- [Shapelet-Based Counterfactual Explanations for Multivariate Time Series](https://mlsanity.com/paper/2208.10462/) (2022)
- [TX-Gen: Multi-Objective Optimization for Sparse Counterfactual Explanations for Time-Series Classification](https://mlsanity.com/paper/2409.09461/) (2024)
- [Multi-SpaCE: Multi-Objective Subsequence-based Sparse Counterfactual Explanations for Multivariate Time Series Classification](https://mlsanity.com/paper/2501.04009/) (2024)

## Abstract (arXiv)

Currently, machine learning is widely used across various domains, including time series data analysis. However, some machine learning models function as black boxes, making interpretability a critical concern. One approach to address this issue is counterfactual explanation (CE), which aims to provide insights into model predictions. This study focuses on the relatively underexplored problem of generating counterfactual explanations for time series forecasting. We propose a method for extracting CEs in time series forecasting using exogenous variables, which are frequently encountered in fields such as business and marketing. In addition, we present methods for analyzing the influence of each variable over an entire time series, generating CEs by altering only specific variables, and evaluating the quality of the resulting CEs. We validate the proposed method through theoretical analysis and empirical experiments, showcasing its accuracy and practical applicability. These contributions are expected to support real-world decision-making based on time series data analysis.