# Causal Forecasting:Generalization Bounds for Autoregressive Models

arXiv: https://arxiv.org/abs/2111.09831 · HTML: https://mlsanity.com/paper/2111.09831/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 63 references that are in the map.
- First posted on arXiv 18 Nov 2021.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representations](https://mlsanity.com/paper/2002.04083/) (2020)
- [Generalization Bounds and Representation Learning for Estimation of Potential Outcomes and Causal Effects](https://mlsanity.com/paper/2001.07426/) (2020)
- [Shapley Flow: A Graph-based Approach to Interpreting Model Predictions](https://mlsanity.com/paper/2010.14592/) (2020)
- [GluonTS: Probabilistic Time Series Models in Python](https://mlsanity.com/paper/1906.05264/) (2019)
- [Regularized estimation in sparse high-dimensional time series models](https://mlsanity.com/paper/1311.4175/) (2013)
- [Off-policy Evaluation in Infinite-Horizon Reinforcement Learning with Latent Confounders](https://mlsanity.com/paper/2007.13893/) (2020)
- [Sequential Deconfounding for Causal Inference with Unobserved Confounders](https://mlsanity.com/paper/2104.09323/) (2021)
- [Causal Regularization](https://mlsanity.com/paper/1906.12179/) (2019)
- [Estimating Structured Vector Autoregressive Model](https://mlsanity.com/paper/1602.06606/) (2016)

## Built on by (most cited first, 5 of 5)

- [Non-Vacuous Generalization Bounds for Large Language Models](https://mlsanity.com/paper/2312.17173/) (2023)
- [Deep Learning based Forecasting: a case study from the online fashion industry](https://mlsanity.com/paper/2305.14406/) (2023)
- [Interpolation and Regularization for Causal Learning](https://mlsanity.com/paper/2202.09054/) (2022)
- [Causal Dynamic Variational Autoencoder for Counterfactual Regression in Longitudinal Data](https://mlsanity.com/paper/2310.10559/) (2023)
- [Learning Joint Interventional Effects from Single-Variable Interventions in Additive Models](https://mlsanity.com/paper/2506.04945/) (2025)

## Abstract (arXiv)

Despite the increasing relevance of forecasting methods, causal implications of these algorithms remain largely unexplored. This is concerning considering that, even under simplifying assumptions such as causal sufficiency, the statistical risk of a model can differ significantly from its textitcausal risk. Here, we study the problem of textitcausal generalization -- generalizing from the observational to interventional distributions -- in forecasting. Our goal is to find answers to the question: How does the efficacy of an autoregressive (VAR) model in predicting statistical associations compare with its ability to predict under interventions? To this end, we introduce the framework of textitcausal learning theory for forecasting. Using this framework, we obtain a characterization of the difference between statistical and causal risks, which helps identify sources of divergence between them. Under causal sufficiency, the problem of causal generalization amounts to learning under covariate shifts, albeit with additional structure (restriction to interventional distributions under the VAR model). This structure allows us to obtain uniform convergence bounds on causal generalizability for the class of VAR models. To the best of our knowledge, this is the first work that provides theoretical guarantees for causal generalization in the time-series setting.