Exact Confidence Intervals for Impulse Responses in a Gaussian Vector Autoregression

Abstract

Many techniques have been proposed for forming confidence intervals for the impulse responses in a vector autoregression. However, numerous Monte-Carlo simulations have shown that all of these methods often have coverage well below the nominal level. This paper proposes a new approach to constructing confidence intervals for impulse responses in a vector autoregression, making the additional assumption of Gaussianity. These confidence intervals are conservative in all sample sizes; by construction they have coverage that must be greater than or equal to the nominal level.

Keywords: Confidence Intervals, Vector Autoregressions, Impulse Responses, Bootstrap