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 Buhlmann (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 @math 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.
@cite_6: Summary Continuous treatments (e.g. doses) arise often in practice, but many available causal effect estimators are limited by either requiring parametric models for the effect curve, or by not allowing doubly robust covariate adjustment. We develop a novel kernel smoothing approach that requires only mild smoothness assumptions on the effect curve and still allows for misspecification of either the treatment density or outcome regression. We derive asymptotic properties and give a procedure for data-driven bandwidth selection. The methods are illustrated via simulation and in a study of the effect of nurse staffing on hospital readmissions penalties.
There is a substantial literature on nonparametric estimation of causal effects of binary treatment or intervention variables . For continuous treatments or intervention variables, recent work also includes @cite_6 , besides the marginal integration approach . Marginal integration itself has been proposed by for smooth function estimation in structured nonparametric regression, mainly for additive models. The theoretical analysis in is the basis for inferring causal effects in the setting of independent data . We are not aware of any other work which considers estimation of causal effects, as defined in , for the setting of stationary time series.