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Working Paper
The Uniform Validity of Impulse Response Inference in Autoregressions
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 ...
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Uniform Inference with General Autoregressive Processes
A unified theory of estimation and inference is developed for an autoregressive process with root in (-∞, ∞) that includes the stationary, local-to-unity, explosive and all intermediate regions. The discontinuity of the limit distribution of the t-statistic outside the stationary region and its dependence on the distribution of the innovations in the explosive regions (-∞, -1) ∪ (1, ∞) are addressed simultaneously. A novel estimation procedure, based on a data-driven combination of a near-stationary and a mildly explosive artificially constructed instrument, delivers mixed-Gaussian ...