TY - JOUR

T1 - Invariant Causal Prediction for Sequential Data

AU - Pfister, Niklas

AU - Bühlmann, Peter

AU - Peters, Jonas

PY - 2019

Y1 - 2019

N2 - We investigate the problem of inferring the causal predictors of a response Y from a set of d explanatory variables (X1, …, Xd). Classical ordinary least-square 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 is the same for all observations, provided that there are no interventions on Y. 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. Supplementary materials for this article are available online.

AB - We investigate the problem of inferring the causal predictors of a response Y from a set of d explanatory variables (X1, …, Xd). Classical ordinary least-square 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 is the same for all observations, provided that there are no interventions on Y. 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. Supplementary materials for this article are available online.

KW - Causal structure learning

KW - Change point model

KW - Chow statistic

KW - Instantaneous causal effects

KW - Monetary policy

UR - http://www.scopus.com/inward/record.url?scp=85058710341&partnerID=8YFLogxK

U2 - 10.1080/01621459.2018.1491403

DO - 10.1080/01621459.2018.1491403

M3 - Journal article

AN - SCOPUS:85058710341

VL - 114

SP - 1264

EP - 1276

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 527

ER -