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Calculating joint confidence bands for impulse response functions using highest density regions

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  • Lütkepohl, Helmut
  • Staszewska-Bystrova, Anna
  • Winker, Peter

Abstract

This paper proposes a new non-parametric method of constructing joint con- dence bands for impulse response functions of vector autoregressive models. The estimation uncertainty is captured by means of bootstrapping and the highest density region (HDR) approach is used to construct the bands. A Monte Carlo comparison of the HDR bands with existing alternatives shows that the former are competitive with the bootstrap-based Bonferroni and Wald con dence regions. The relative tightness of the HDR bands matched with their good coverage properties makes them attractive for applications. An application to corporate bond spreads for Germany highlights the potential for empirical work.

Suggested Citation

  • Lütkepohl, Helmut & Staszewska-Bystrova, Anna & Winker, Peter, 2016. "Calculating joint confidence bands for impulse response functions using highest density regions," SFB 649 Discussion Papers 2016-017, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2016-017
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    References listed on IDEAS

    as
    1. Inoue, Atsushi & Kilian, Lutz, 2016. "Joint confidence sets for structural impulse responses," Journal of Econometrics, Elsevier, vol. 192(2), pages 421-432.
    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, Central European Journal of Economic Modelling and Econometrics, vol. 6(2), pages 89-104, June.
    3. repec:diw:diwwpp:dp1354 is not listed on IDEAS
    4. Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
    5. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2014. "Confidence Bands for Impulse Responses: Bonferroni versus Wald," Discussion Papers of DIW Berlin 1354, DIW Berlin, German Institute for Economic Research.
    6. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    7. Staszewska-Bystrova, Anna & Winker, Peter, 2013. "Constructing narrowest pathwise bootstrap prediction bands using threshold accepting," International Journal of Forecasting, Elsevier, vol. 29(2), pages 221-233.
    8. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2015. "Confidence Bands for Impulse Responses: Bonferroni vs. Wald," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(6), pages 800-821, December.
    9. Staszewska-Bystrova Anna, 2013. "Modified Scheffé’s Prediction Bands," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 233(5-6), pages 680-690, October.
    10. 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.
    11. Fresoli, Diego & Ruiz, Esther & Pascual, Lorenzo, 2015. "Bootstrap multi-step forecasts of non-Gaussian VAR models," International Journal of Forecasting, Elsevier, vol. 31(3), pages 834-848.
    12. Lütkepohl, Helmut & Staszewska-Bystrova, Anna & Winker, Peter, 2014. "Confidence bands for impulse responses: Bonferroni versus Wald," SFB 649 Discussion Papers 2014-007, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
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    Citations

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    Cited by:

    1. Inoue, Atsushi & Kilian, Lutz, 2020. "The uniform validity of impulse response inference in autoregressions," Journal of Econometrics, Elsevier, vol. 215(2), pages 450-472.
    2. 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.
    3. Kilian, Lutz & Inoue, Atsushi, 2020. "The Role of the Prior in Estimating VAR Models with Sign Restrictions," CEPR Discussion Papers 15545, C.E.P.R. Discussion Papers.
    4. Jonas E. Arias & Juan F. Rubio-Ramirez & Daniel F. Waggoner, 2020. "Uniform Priors for Impulse Responses," Working Papers 22-30, Federal Reserve Bank of Philadelphia.
    5. Mardi Dungey & Denise R. Osborn, 2020. "The Gains from Catch‐up for China and the USA: An Empirical Framework," The Economic Record, The Economic Society of Australia, vol. 96(314), pages 350-365, September.
    6. Inoue, Atsushi & Kilian, Lutz, 2022. "Joint Bayesian inference about impulse responses in VAR models," Journal of Econometrics, Elsevier, vol. 231(2), pages 457-476.

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    More about this item

    Keywords

    impulse responses; joint confidence bands; highest density region; vector autoregressive process;
    All these keywords.

    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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