Vector Autoregressions and Reality

This article questions the statistical significance of variance decompositions and impulse response functions for unrestricted vector autoregressions. It suggests that previous authors have failed to provide confidence intervals for variance decompositions and impulse response functions. Two methods of computing such confidence intervals are developed: first, using a normal approximation; second, using bootstrapped resampling. An example from Sims's work is used to illustrate the importance of computing these confidence intervals. In this example, the 95% confidence intervals for variance decompositions span up to 66 percentage points at the usual forecasting horizon.