# Identifying Causal Effects using Instrumental Time Series: Nuisance IV and Correcting for the Past

arXiv: https://arxiv.org/abs/2203.06056 · HTML: https://mlsanity.com/paper/2203.06056/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 72 references that are in the map.
- First posted on arXiv 11 Mar 2022.

## Builds on (most cited first, 8 of 8)

- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Anchor regression: heterogeneous data meets causality](https://mlsanity.com/paper/1801.06229/) (2018)
- [A causal framework for distribution generalization](https://mlsanity.com/paper/2006.07433/) (2020)
- [Causal models for dynamical systems](https://mlsanity.com/paper/2001.06208/) (2020)
- [Exploiting Independent Instruments: Identification and Distribution Generalization](https://mlsanity.com/paper/2202.01864/) (2022)
- [Causal Discovery from Subsampled Time Series Data by Constraint Optimization](https://mlsanity.com/paper/1602.07970/) (2016)
- [Distributional robustness of K-class estimators and the PULSE](https://mlsanity.com/paper/2005.03353/) (2020)
- [Invariant Models for Causal Transfer Learning](https://mlsanity.com/paper/1507.05333/) (2015)

## Built on by (most cited first, 9 of 9)

- [Towards Trustworthy and Aligned Machine Learning: A Data-centric Survey with Causality Perspectives](https://mlsanity.com/paper/2307.16851/) (2023)
- [Estimating Direct and Indirect Causal Effects of Spatiotemporal Interventions in Presence of Spatial Interference](https://mlsanity.com/paper/2405.08174/) (2024)
- [Quantifying Causes of Arctic Amplification via Deep Learning based Time-series Causal Inference](https://mlsanity.com/paper/2303.07122/) (2023)
- [Causality for Earth Science -- A Review on Time-series and Spatiotemporal Causality Methods](https://mlsanity.com/paper/2404.05746/) (2024)
- [DecoR: Deconfounding Time Series with Robust Regression](https://mlsanity.com/paper/2406.07005/) (2024)
- [Identifying Elasticities in Autocorrelated Time Series Using Causal Graphs](https://mlsanity.com/paper/2409.15530/) (2024)
- [Projecting infinite time series graphs to finite marginal graphs using number theory](https://mlsanity.com/paper/2310.05526/) (2023)
- [Leaning Time-Varying Instruments for Identifying Causal Effects in Time-Series Data](https://mlsanity.com/paper/2411.17774/) (2024)
- [Using Time Structure to Estimate Causal Effects](https://mlsanity.com/paper/2504.11076/) (2025)

## Abstract (arXiv)

Instrumental variable (IV) regression relies on instruments to infer causal effects from observational data with unobserved confounding. We consider IV regression in time series models, such as vector auto-regressive (VAR) processes. Direct applications of i.i.d. techniques are generally inconsistent as they do not correctly adjust for dependencies in the past. In this paper, we outline the difficulties that arise due to time structure and propose methodology for constructing identifying equations that can be used for consistent parametric estimation of causal effects in time series data. One method uses extra nuisance covariates to obtain identifiability (an idea that can be of interest even in the i.i.d. case). We further propose a graph marginalization framework that allows us to apply nuisance IV and other IV methods in a principled way to time series. Our methods make use of a version of the global Markov property, which we prove holds for VAR(p) processes. For VAR(1) processes, we prove identifiability conditions that relate to Jordan forms and are different from the well-known rank conditions in the i.i.d. case (they do not require as many instruments as covariates, for example). We provide methods, prove their consistency, and show how the inferred causal effect can be used for distribution generalization. Simulation experiments corroborate our theoretical results. We provide ready-to-use Python code.