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The uniform validity of impulse response inference in autoregressions

Author

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  • Atsushi Inoue

    () (Vanderbilt University)

  • Lutz Kilian

    () (University of Michigan)

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.

Suggested Citation

  • Atsushi Inoue & Lutz Kilian, 2019. "The uniform validity of impulse response inference in autoregressions," Vanderbilt University Department of Economics Working Papers 19-00001, Vanderbilt University Department of Economics.
  • Handle: RePEc:van:wpaper:vuecon-sub-19-00001
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    References listed on IDEAS

    as
    1. Atsushi Inoue & Lutz Kilian, 2002. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometrica, Econometric Society, vol. 70(1), pages 377-391, January.
    2. Bauer, Dietmar & Maynard, Alex, 2012. "Persistence-robust surplus-lag Granger causality testing," Journal of Econometrics, Elsevier, vol. 169(2), pages 293-300.
    3. Inoue, Atsushi & Kilian, Lutz, 2003. "The Continuity Of The Limit Distribution In The Parameter Of Interest Is Not Essential For The Validity Of The Bootstrap," Econometric Theory, Cambridge University Press, vol. 19(6), pages 944-961, December.
    4. Phillips, Peter C.B. & Lee, Ji Hyung, 2016. "Robust econometric inference with mixed integrated and mildly explosive regressors," Journal of Econometrics, Elsevier, vol. 192(2), pages 433-450.
    5. Anna Mikusheva, 2012. "One‚ÄźDimensional Inference in Autoregressive Models With the Potential Presence of a Unit Root," Econometrica, Econometric Society, vol. 80(1), pages 173-212, January.
    6. Lutz Kilian, 1999. "Finite-Sample Properties of Percentile and Percentile-t Bootstrap Confidence Intervals for Impulse Responses," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 652-660, November.
    7. Toda, Hiro Y. & Yamamoto, Taku, 1995. "Statistical inference in vector autoregressions with possibly integrated processes," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 225-250.
    8. Alexander Benkwitz & Michael Neumann & Helmut Lutekpohl, 2000. "Problems related to confidence intervals for impulse responses of autoregressive processes," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 69-103.
    9. Stefan Bruder & Michael Wolf, 2017. "Balanced bootstrap joint confidence bands for structural impulse response functions," ECON - Working Papers 246, Department of Economics - University of Zurich, revised Jan 2018.
    10. repec:cup:cbooks:9781316647332 is not listed on IDEAS
    11. repec:bpj:jecome:v:8:y:2019:i:1:p:19:n:9 is not listed on IDEAS
    12. Kilian, Lutz & Chang, Pao-Li, 2000. "How accurate are confidence intervals for impulse responses in large VAR models?," Economics Letters, Elsevier, vol. 69(3), pages 299-307, December.
    13. repec:cup:cbooks:9781107196575 is not listed on IDEAS
    14. Kasy Maximilian, 2019. "Uniformity and the Delta Method," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-19, January.
    15. repec:eee:econom:v:203:y:2018:i:2:p:316-327 is not listed on IDEAS
    16. Nankervis, J C & Savin, N E, 1988. "The Student's t Approximation in a Stationary First Order Autoregressive Model," Econometrica, Econometric Society, vol. 56(1), pages 119-145, January.
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    More about this item

    Keywords

    Impulse response; autoregression; lag augmentation; asymptotic normality; bootstrap; uniform inference;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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