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Confidence Bands for Impulse Responses: Bonferroni versus Wald

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  • Helmut Lütkepohl
  • Anna Staszewska-Bystrova
  • Peter Winker

Abstract

In impulse response analysis estimation uncertainty is typically displayed by constructing bands around estimated impulse response functions. These bands may be based on frequentist or Bayesian methods. If they are based on the joint distribution in the Bayesian framework or the joint asymptotic distribution possibly constructed with bootstrap methods in the frequentist framework often individual confidence intervals or credibility sets are simply connected to obtain the bands. Such bands are known to be too narrow and have a joint confidence content lower than the desired one. If instead the joint distribution of the impulse response coefficients is taken into account and mapped into the band it is shown that such a band is typically rather conservative. It is argued that a smaller band can often be obtained by using the Bonferroni method. While these considerations are equally important for constructing forecast bands, we focus on the case of impulse responses in this study.

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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2014-007.

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Length: 33 pages
Date of creation: Jan 2014
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Handle: RePEc:hum:wpaper:sfb649dp2014-007

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Keywords: Impulse responses; Bayesian error bands; frequentist confidence bands; Wald statistic; vector autoregressive process;

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References

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  1. �scar Jord� & Massimiliano Marcellino, 2010. "Path forecast evaluation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 25(4), pages 635-662.
  2. Inoue, Atsushi & Kilian, Lutz, 2011. "Inference on Impulse Response Functions in Structural VAR Models," CEPR Discussion Papers 8419, C.E.P.R. Discussion Papers.
  3. Kilian, Lutz, 2006. "Not All Oil Price Shocks Are Alike: Disentangling Demand and Supply Shocks in the Crude Oil Market," CEPR Discussion Papers 5994, C.E.P.R. Discussion Papers.
  4. Staszewska-Bystrova, Anna & Winker, Peter, 2013. "Constructing narrowest pathwise bootstrap prediction bands using threshold accepting," International Journal of Forecasting, Elsevier, Elsevier, vol. 29(2), pages 221-233.
  5. Jae H. Kim, 2004. "Bias-corrected bootstrap prediction regions for vector autoregression," Journal of Forecasting, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 23(2), pages 141-154.
  6. 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.
  7. Staszewska, Anna, 2007. "Representing uncertainty about response paths: The use of heuristic optimisation methods," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 52(1), pages 121-132, September.
  8. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2013. "Comparison of Methods for Constructing Joint Confidence Bands for Impulse Response Functions," Discussion Papers of DIW Berlin 1292, DIW Berlin, German Institute for Economic Research.
  9. Bernanke, Ben S. & Mihov, Ilian, 1995. "Measuring Monetary Policy," Economics Series 10, Institute for Advanced Studies.
  10. Uhlig, Harald, 2005. "What are the effects of monetary policy on output? Results from an agnostic identification procedure," Journal of Monetary Economics, Elsevier, Elsevier, vol. 52(2), pages 381-419, March.
  11. Anna Staszewska‐Bystrova, 2011. "Bootstrap prediction bands for forecast paths from vector autoregressive models," Journal of Forecasting, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 30(8), pages 721-735, December.
  12. Christopher A. Sims & Tao Zha, 1994. "Error Bands for Impulse Responses," Cowles Foundation Discussion Papers 1085, Cowles Foundation for Research in Economics, Yale University.
  13. Kim, Jae H., 1999. "Asymptotic and bootstrap prediction regions for vector autoregression," International Journal of Forecasting, Elsevier, Elsevier, vol. 15(4), pages 393-403, October.
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Cited by:
  1. Atsushi Inoue & Lutz Kilian, 2014. "Joint Confidence Sets for Structural Impulse Responses," Departmental Working Papers 1401, Southern Methodist University, Department of Economics.
  2. Anna Staszewska-Bystrova & Peter Winker, 2014. "Measuring Forecast Uncertainty of Corporate Bond Spreads by Bonferroni-Type Prediction Bands," Central European Journal of Economic Modelling and Econometrics, CEJEME, CEJEME, vol. 6(2), pages 89-104, June.

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