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The uniform validity of impulse response inference in autoregressions

Atsushi Inoue () and Lutz Kilian ()

No 19-00001, Vanderbilt University Department of Economics Working Papers from Vanderbilt University Department of Economics

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 at fixed horizons. 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 resulting confidence intervals remain accurate even at long horizons. We provide a formal asymptotic justification for this result.

Keywords: Impulse response; autoregression; lag augmentation; asymptotic normality; bootstrap; uniform inference (search for similar items in EconPapers)
JEL-codes: C22 C52 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm and nep-ets
Date: 2019-03-25
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Related works:
Working Paper: The Uniform Validity of Impulse Response Inference in Autoregressions (2019) Downloads
Working Paper: The uniform validity of impulse response inference in autoregressions (2019) Downloads
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