Granger Causality, Impulse Responses, and Forecast Error Variance Decomposition

After fitting a VAR, a portfolio team wants more than a collection of lag matrices. It wants to know whether macro news improves equity-return forecasts, how a rate innovation travels through a curve-risk book, and what fraction of a forecast miss comes from each innovation. Granger tests, impulse responses, and forecast error variance decompositions (FEVDs) answer these three distinct questions. They are useful summaries of a fitted system, but none turns a predictive association into an economic causal claim.

• formulate and test a block-exogeneity restriction in a VAR;
• state exactly what Granger causality does and does not establish;
• derive the moving-average form used to construct impulse responses;
• interpret an FEVD at a stated forecast horizon;
• explain why correlated reduced-form innovations require an identification choice before interpreting orthogonalised responses.

1. Granger causality is incremental predictability
2. From a VAR shock to an impulse response
3. Forecast error variance decomposition
4. A disciplined interpretation workflow