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Confidence Bands for Impulse Responses: Bonferroni versus Wald

Author

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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.

Suggested Citation

  • Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2014. "Confidence Bands for Impulse Responses: Bonferroni versus Wald," SFB 649 Discussion Papers SFB649DP2014-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2014-007
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    References listed on IDEAS

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    Cited by:

    1. 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, vol. 6(2), pages 89-104, June.
    2. Inoue, Atsushi & Kilian, Lutz, 2016. "Joint confidence sets for structural impulse responses," Journal of Econometrics, Elsevier, vol. 192(2), pages 421-432.
    3. Neil Kellard & Denise Osborn & Jerry Coakley & Simone D. Grose & Gael M. Martin & Donald S. Poskitt, 2015. "Bias Correction of Persistence Measures in Fractionally Integrated Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 721-740, September.
    4. Haug, Alfred A. & King, Ian, 2014. "In the long run, US unemployment follows inflation like a faithful dog," Journal of Macroeconomics, Elsevier, vol. 41(C), pages 42-52.

    More about this item

    Keywords

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

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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