On Counterfactual Interventions in Vector Autoregressive Models

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.