Title: Invariant Causal Prediction for Sequential Data,
Abstract: We investigate the problem of inferring the causal predictors of a response
$Y$ from a set of $d$ explanatory variables $(X^1,\dots,X^d)$. Classical
ordinary least squares regression includes all predictors that reduce the
variance of $Y$. Using only the causal predictors instead leads to models that
have the advantage of remaining invariant under interventions, loosely speaking
they lead to invariance across different "environments" or "heterogeneity
patterns". More precisely, the conditional distribution of $Y$ given its causal
predictors remains invariant for all observations. Recent work exploits such a
stability to infer causal relations from data with different but known
environments. We show that even without having knowledge of the environments or
heterogeneity pattern, inferring causal relations is possible for time-ordered
(or any other type of sequentially ordered) data. In particular, this allows
detecting instantaneous causal relations in multivariate linear time series
which is usually not the case for Granger causality. Besides novel methodology,
we provide statistical confidence bounds and asymptotic detection results for
inferring causal predictors, and present an application to monetary policy in
macroeconomics.