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Problems related to confidence intervals for impulse responses of autoregressive processes


  • Alexander Benkwitz
  • Michael Neumann
  • Helmut Lutekpohl


Confidence intervals for impulse responses computed from autoregressive processes are considered. A detailed analysis of the methods in current use shows that they are not very reliable in some cases. In particular, there are theoretical reasons for them to have actual coverage probabilities which deviate considerably from the nominal level in some situations of practical importance. For a simple case alternative bootstrap methods are proposed which provide correct results asymptotically.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:emetrv:v:19:y:2000:i:1:p:69-103 DOI: 10.1080/07474930008800460

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    References listed on IDEAS

    1. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
    2. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(03), pages 361-376, June.
    3. Davidson, Russell & MacKinnon, James G, 1998. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," The Manchester School of Economic & Social Studies, University of Manchester, vol. 66(1), pages 1-26, January.
    4. Donald W. K. Andrews & Moshe Buchinsky, 2000. "A Three-Step Method for Choosing the Number of Bootstrap Repetitions," Econometrica, Econometric Society, vol. 68(1), pages 23-52, January.
    5. Jean-Marie Dufour & Jan F. Kiviet, 1998. "Exact Inference Methods for First-Order Autoregressive Distributed Lag Models," Econometrica, Econometric Society, vol. 66(1), pages 79-104, January.
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    Cited by:

    1. DUFOUR, Jean-Marie & JOUINI, Tarek, 2005. "Finite-Sample Simulation-Based Inference in VAR Models with Applications to Order Selection and Causality Testing," Cahiers de recherche 16-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. 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.
    3. Dufour, Jean-Marie, 2006. "Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics," Journal of Econometrics, Elsevier, vol. 133(2), pages 443-477, August.
    4. Hess, Martin K., 2004. "Dynamic and asymmetric impacts of macroeconomic fundamentals on an integrated stock market," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 14(5), pages 455-471, December.
    5. Brüggemann, Ralf & Jentsch, Carsten & Trenkler, Carsten, 2016. "Inference in VARs with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 191(1), pages 69-85.
    6. Dufour, Jean-Marie & Jouini, Tarek, 2006. "Finite-sample simulation-based inference in VAR models with application to Granger causality testing," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 229-254.
    7. repec:spr:empeco:v:53:y:2017:i:4:d:10.1007_s00181-016-1184-3 is not listed on IDEAS
    8. Müller, Gernot J., 2008. "Understanding the dynamic effects of government spending on foreign trade," Journal of International Money and Finance, Elsevier, vol. 27(3), pages 345-371, April.
    9. Zavale, Helder & Myers, Robert & Tschirley, David, 2015. "Market Level Effects of World Food Program Local and Regional Procurement of Food Aid in Africa," 2015 Conference, August 9-14, 2015, Milan, Italy 211862, International Association of Agricultural Economists.
    10. Kilian, Lutz & Kim, Yun Jung, 2009. "Do Local Projections Solve the Bias Problem in Impulse Response Inference?," CEPR Discussion Papers 7266, C.E.P.R. Discussion Papers.
    11. Brüggemann, Ralf & Lütkepohl, Helmut, 2000. "Lag selection in subset VAR models with an application to a US monetary system," SFB 373 Discussion Papers 2000,37, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    12. Tuck Cheong Tang, 2006. "Japan's balancing item: do timing errors matter?," Applied Economics Letters, Taylor & Francis Journals, vol. 13(2), pages 81-87.
    13. Mei-yin Lin & Hui-hua Wang, 2009. "What Causes the Volatility of the Balancing Item?," Economics Bulletin, AccessEcon, vol. 29(4), pages 2738-2748.
    14. Tschirley, David & Myers, Robert & Zavale, Helder, 2014. "MSU/FSG Study of the Impact of WFP Local and Regional Food Aid Procurement on Markets, Households, and Food Value Chains," Food Security International Development Working Papers 184835, Michigan State University, Department of Agricultural, Food, and Resource Economics.
    15. Müller, Christian, 2012. "A new interpretation of known facts: The case of two-way causality between trading and volatility," Economic Modelling, Elsevier, vol. 29(3), pages 664-670.
    16. Granger, Clive W. J. & Jeon, Yongil, 2004. "Thick modeling," Economic Modelling, Elsevier, vol. 21(2), pages 323-343, March.
    17. Tuck Cheong Tang, 2006. "The influences of economic openness on Japan's balancing item: an empirical note," Applied Economics Letters, Taylor & Francis Journals, vol. 13(1), pages 7-10.
    18. Herzer, Dierk & Nowak-Lehmann, Felicitas & Dreher, Axel & Klasen, Stephan & Martinez-Zarzoso, Inmaculada, 2015. "Comment on Lof, Mekasha, and Tarp (2014)," World Development, Elsevier, vol. 70(C), pages 389-396.


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