The Uniform Validity of Impulse Response Inference in Autoregressions

Abstract

Existing proofs of the asymptotic validity of conventional methods of impulse response inference based on higher-order autoregressions are pointwise only. In this paper, we establish the uniform asymptotic validity of conventional asymptotic and bootstrap inference about individual impulse responses and vectors of impulse responses when the horizon is fixed with respect to the sample size. For inference about vectors of impulse responses based on Wald test statistics to be uniformly valid, lag-augmented autoregressions are required, whereas inference about individual impulse responses is uniformly valid under weak conditions even without lag augmentation. We introduce a new rank condition that ensures the uniform validity of inference on impulse responses and show that this condition holds under weak conditions. Simulations show that the highest finite-sample accuracy is achieved when bootstrapping the lag-augmented autoregression using the bias adjustments of Kilian (1999). The conventional bootstrap percentile interval for impulse responses based on this approach remains accurate even at long horizons. We provide a formal asymptotic justification for this result.