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Problems related to confidence intervals for impulse responses of autoregressive processes

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  • Alexander Benkwitz
  • Michael Neumann
  • Helmut Lutekpohl

Abstract

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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    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, 2018. "Balanced Bootstrap Joint Confidence Bands for Structural Impulse Response Functions," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(5), pages 641-664, September.
    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. Daniel Grabowski & Anna Staszewska-Bystrova & Peter Winker, 2020. "Skewness-adjusted bootstrap confidence intervals and confidence bands for impulse response functions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 5-32, March.
    6. 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.
    7. Minxian Yang, 2017. "Effects of idiosyncratic shocks on macroeconomic time series," Empirical Economics, Springer, vol. 53(4), pages 1441-1461, December.
    8. Lütkepohl, Helmut & Staszewska-Bystrova, Anna & Winker, Peter, 2020. "Constructing joint confidence bands for impulse response functions of VAR models – A review," Econometrics and Statistics, Elsevier, vol. 13(C), pages 69-83.
    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. Carsten Trenkler & Enzo Weber, 2020. "Identifying shocks to business cycles with asynchronous propagation," Empirical Economics, Springer, vol. 58(4), pages 1815-1836, April.
    13. Tuck Cheong Tang, 2006. "Japan's balancing item: do timing errors matter?," Applied Economics Letters, Taylor & Francis Journals, vol. 13(2), pages 81-87.
    14. Mei-yin Lin & Hui-hua Wang, 2009. "What Causes the Volatility of the Balancing Item?," Economics Bulletin, AccessEcon, vol. 29(4), pages 2738-2748.
    15. José Luis Montiel Olea & Mikkel Plagborg‐Møller, 2021. "Local Projection Inference Is Simpler and More Robust Than You Think," Econometrica, Econometric Society, vol. 89(4), pages 1789-1823, July.
    16. Inoue, Atsushi & Kilian, Lutz, 2020. "The uniform validity of impulse response inference in autoregressions," Journal of Econometrics, Elsevier, vol. 215(2), pages 450-472.
    17. 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.
    18. Granger, Clive W. J. & Jeon, Yongil, 2004. "Thick modeling," Economic Modelling, Elsevier, vol. 21(2), pages 323-343, March.
    19. 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.
    20. 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.
    21. 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.
    22. Haffar, Adlane & Le Fur, Eric, 2021. "Structural vector error correction modelling of Bitcoin price," The Quarterly Review of Economics and Finance, Elsevier, vol. 80(C), pages 170-178.
    23. 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.
    24. 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.
    25. Gafarov, Bulat & Meier, Matthias & Montiel Olea, José Luis, 2018. "Delta-method inference for a class of set-identified SVARs," Journal of Econometrics, Elsevier, vol. 203(2), pages 316-327.

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