# Causal Inference by Identification of Vector Autoregressive Processes with Hidden Components

arXiv: https://arxiv.org/abs/1411.3972 · HTML: https://mlsanity.com/paper/1411.3972/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2014.

## Built on by (most cited first, 11 of 11)

- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Learning the Causal Structure of Networked Dynamical Systems under Latent Nodes and Structured Noise](https://mlsanity.com/paper/2312.05974/) (2023)
- [Causal Inference for Banking Finance and Insurance A Survey](https://mlsanity.com/paper/2307.16427/) (2023)
- [A Practical Approach to Causal Inference over Time](https://mlsanity.com/paper/2410.10502/) (2024)
- [Federated Granger Causality Learning for Interdependent Clients with State Space Representation](https://mlsanity.com/paper/2501.13890/) (2025)
- [Recovering the Graph Underlying Networked Dynamical Systems under Partial Observability: A Deep Learning Approach](https://mlsanity.com/paper/2208.04405/) (2022)
- [Information Theoretic Measures of Causal Influences during Transient Neural Events](https://mlsanity.com/paper/2209.07508/) (2022)
- [Temporal Latent Variable Structural Causal Model for Causal Discovery under External Interferences](https://mlsanity.com/paper/2511.10031/) (2025)
- [The Powers of Precision: Structure-Informed Detection in Complex Systems -- From Customer Churn to Seizure Onset](https://mlsanity.com/paper/2601.21170/) (2026)
- [Learning Unknown Interdependencies for Decentralized Root Cause Analysis in Nonlinear Dynamical Systems](https://mlsanity.com/paper/2602.21928/) (2026)
- [Function-Valued Causal Influence in Nonlinear Time Series](https://mlsanity.com/paper/2605.26408/) (2026)

## Abstract (arXiv)

A widely applied approach to causal inference from a non-experimental time series X, often referred to as "(linear) Granger causal analysis", is to regress present on past and interpret the regression matrix hatB causally. However, if there is an unmeasured time series Z that influences X, then this approach can lead to wrong causal conclusions, i.e., distinct from those one would draw if one had additional information such as Z. In this paper we take a different approach: We assume that X together with some hidden Z forms a first order vector autoregressive (VAR) process with transition matrix A, and argue why it is more valid to interpret A causally instead of hatB. Then we examine under which conditions the most important parts of A are identifiable or almost identifiable from only X. Essentially, sufficient conditions are (1) non-Gaussian, independent noise or (2) no influence from X to Z. We present two estimation algorithms that are tailored towards conditions (1) and (2), respectively, and evaluate them on synthetic and real-world data. We discuss how to check the model using X.