  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.
