Nonparametric causal inference from observational time series through marginal integration

TL;DR

This paper introduces MINT-T, a nonparametric method for causal inference in stationary time series, capable of estimating causal effects with optimal convergence rates and handling instantaneous effects to prevent false positives.

Contribution

It adapts a nonparametric causal inference method for time series, achieving optimal convergence and addressing instantaneous effects, expanding applicability to nonlinear and multivariate processes.

Findings

Consistently recovers total causal effect with rate n^{-2/5}

Applicable to nonlinear and multivariate stationary time series

Provides a procedure to avoid false positives with instantaneous effects

Abstract

Causal inference from observational data is an ambitious but highly relevant task, with diverse applications ranging from natural to social sciences. Within the scope of nonparametric time series, causal inference defined through interventions (cf. Pearl (2000)) is largely unexplored, although time order simplifies the problem substantially. We consider a marginal integration scheme for inferring causal effects from observational time series data, MINT-T (marginal integration in time series), which is an adaptation for time series of a method proposed by Ernest and B\"{u}hlmann (Electron. J. Statist, pp. 3155-3194, vol. 9, 2015) for the case of independent data. Our approach for stationary stochastic processes is fully nonparametric and, assuming no instantaneous effects consistently recovers the total causal effect of a single intervention with optimal one-dimensional nonparametric convergence rate $n^{-2/5}$ assuming regularity conditions and twice differentiability of a certain corresponding regression function. Therefore, MINT-T remains largely unaffected by the curse of dimensionality as long as smoothness conditions hold in higher dimensions and it is feasible for a large class of stationary time series, including nonlinear and multivariate processes. For the case with instantaneous effects, we provide a procedure which guards against false positive causal statements.