Causal Inference by Identification of Vector Autoregressive Processes with Hidden Components

TL;DR

This paper proposes a new approach to causal inference in time series by modeling the joint process of observed and hidden variables as a VAR process, enabling more accurate causal interpretation under certain conditions.

Contribution

It introduces a framework for causal inference using VAR models with hidden components and provides algorithms for identifying the transition matrix under specific assumptions.

Findings

Conditions for identifiability of the transition matrix A.

Two algorithms tailored for different noise and influence conditions.

Evaluation on synthetic and real-world data demonstrating effectiveness.

Abstract

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 $\hat{B}$ 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 $\hat{B}$. 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 $X$.