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Exact confidence intervals for impulse responses in a Gaussian vector autoregression

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  • Jonathan H. Wright

Abstract

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.

Suggested Citation

  • Jonathan H. Wright, 2000. "Exact confidence intervals for impulse responses in a Gaussian vector autoregression," International Finance Discussion Papers 682, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgif:682
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    References listed on IDEAS

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    1. Runkle, David E, 1987. "Vector Autoregressions and Reality," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 437-442, October.
    2. 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.
    3. Christopher A. Sims & Tao Zha, 1999. "Error Bands for Impulse Responses," Econometrica, Econometric Society, vol. 67(5), pages 1113-1156, September.
    4. David E. Runkle, 1987. "Vector autoregressions and reality," Staff Report 107, Federal Reserve Bank of Minneapolis.
    5. Campbell, Bryan & Dufour, Jean-Marie, 1997. "Exact Nonparametric Tests of Orthogonality and Random Walk in the Presence of a Drift Parameter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 151-173, February.
    6. 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.
    7. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-165, January.
    8. 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 368-373, July.
    9. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    10. 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.
    11. Lutz Kilian, 1998. "Confidence intervals for impulse responses under departures from normality," Econometric Reviews, Taylor & Francis Journals, vol. 17(1), pages 1-29.
    12. Runkle, David E, 1987. "Vector Autoregressions and Reality: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 454-454, October.
    13. 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 116-125, February.
    14. 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.
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    Cited by:

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    2. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
    3. Ossama Mikhail & Curtis J. Eberwein & Jagdish Handa, 2003. "Can Sectoral Shifts Generate Persistent Unemployment in Real Business Cycle Models?," Macroeconomics 0311004, University Library of Munich, Germany.

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    Keywords

    Vector autoregression; Macroeconomics;

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