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Exact confidence intervals for impulse responses in a Gaussian vector autoregression

  • Jonathan H. Wright

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.

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Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series International Finance Discussion Papers with number 682.

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Date of creation: 2000
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Handle: RePEc:fip:fedgif:682
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  1. Lutkepohl, Helmut, 1990. "Asymptotic Distributions of Impulse Response Functions and Forecast Error Variance Decompositions of Vector Autoregressive Models," The Review of Economics and Statistics, MIT Press, vol. 72(1), pages 116-25, February.
  2. Christopher A. Sims & Tao Zha, 1995. "Error bands for impulse responses," Working Paper 95-6, Federal Reserve Bank of Atlanta.
  3. Phillips, Peter C. B., 1998. "Impulse response and forecast error variance asymptotics in nonstationary VARs," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 21-56.
  4. Bruce E. Hansen, 1999. "The Grid Bootstrap And The Autoregressive Model," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 594-607, November.
  5. Campbell, B. & Dufour, J.M., 1994. "Excat Nonparametric Tests of Orthogonality and Random Walk in the Presence of a Drift Parameter," Cahiers de recherche 9407, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  6. Lutz Kilian, 1998. "Confidence intervals for impulse responses under departures from normality," Econometric Reviews, Taylor & Francis Journals, vol. 17(1), pages 1-29.
  7. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
  8. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-65, January.
  9. Runkle, David E, 1987. "Vector Autoregressions and Reality," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 437-42, October.
  10. David E. Runkle, 1987. "Vector autoregressions and reality," Staff Report 107, Federal Reserve Bank of Minneapolis.
  11. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May.
  12. Wright, Jonathan H, 2000. "Confidence Intervals for Univariate Impulse Responses with a Near Unit Root," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 368-73, July.
  13. 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.
  14. Runkle, David E, 1987. "Vector Autoregressions and Reality: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 454, October.
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