  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.
