  Despite the increasing relevance of forecasting methods, causal implications
of these algorithms remain largely unexplored. This is concerning considering
that, even under simplifying assumptions such as causal sufficiency, the
statistical risk of a model can differ significantly from its \textit{causal
risk}. Here, we study the problem of \textit{causal generalization} --
generalizing from the observational to interventional distributions -- in
forecasting. Our goal is to find answers to the question: How does the efficacy
of an autoregressive (VAR) model in predicting statistical associations compare
with its ability to predict under interventions?
  To this end, we introduce the framework of \textit{causal learning theory}
for forecasting. Using this framework, we obtain a characterization of the
difference between statistical and causal risks, which helps identify sources
of divergence between them. Under causal sufficiency, the problem of causal
generalization amounts to learning under covariate shifts, albeit with
additional structure (restriction to interventional distributions under the VAR
model). This structure allows us to obtain uniform convergence bounds on causal
generalizability for the class of VAR models. To the best of our knowledge,
this is the first work that provides theoretical guarantees for causal
generalization in the time-series setting.
