  Counterfactual reasoning allows us to explore hypothetical scenarios in order
to explain the impacts of our decisions. However, addressing such inquires is
impossible without establishing the appropriate mathematical framework. In this
work, we introduce the problem of counterfactual reasoning in the context of
vector autoregressive (VAR) processes. We also formulate the inference of a
causal model as a joint regression task where for inference we use both data
with and without interventions. After learning the model, we exploit linearity
of the VAR model to make exact predictions about the effects of counterfactual
interventions. Furthermore, we quantify the total causal effects of past
counterfactual interventions. The source code for this project is freely
available at https://github.com/KurtButler/counterfactual_interventions.
