Causal inference in time series settings under the Rubin Causal Model

Causal inference in time series settings is a challenging task, partly because a simple association may be easily mistaken for a causal nexus and partly due to serial dependence, which brings additional difficulties during the estimation process. Having its roots in the potential outcomes framework, we believe that the Rubin Causal Model (RCM) can aid the estimation of causal effects in such settings. Indeed, the RCM allows the construction of "what if" scenarios and sets the theoretical foundations underneath the attribution of the uncovered effect to a specific intervention. In this research we analyze three situations: i) a single intervention occurring simultaneously on multiple non-interfering series; ii) multiple time series subject to a simultaneous treatment that, due to cross-unit interactions, may affect other series that were not intervened on; iii) multiple interventions on a single time series. We introduce a common causal framework building the theoretical foundations for a causal analysis under the RCM; we define new classes of causal estimands and we propose to estimate them using two novel methodologies: C-ARIMA and CausalMBSTS. The C-ARIMA approach can successfully estimate the effect of an intervention on a single time series as well as on multiple non-interfering series. Indeed, with a simulation study we showed that it performs well compared to a standard intervention analysis method in a situation where the effect takes the form of a fixed change in the level of the outcome; it also outperforms the latter when the effects are irregular and time-varying. Instead, CausalMBSTS can estimate the heterogeneous causal effect of an intervention in a panel setting where the time series interact with one another. Based on multivariate Bayesian models, it is a flexible methodology that allows to model the dependence structure between the time series in a very natural way, whilst enabling variable selection (via the addition of a spike-and-slab prior) and validation (by posterior predictive checks). Finally, we showed how to extend the C-ARIMA approach for the estimation of the heterogeneous causal effects of multiple interventions occurring on a single time series. This research brings both methodological and empirical contributions, introducing two novel approaches to infer causal effects in complex time series settings and showing that the proposed methodologies can be employed in several fields of research, including marketing and finance.