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

Author

Listed:
  • 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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    Cited by:

    1. Jonas E. Arias & Juan F. Rubio‐Ramírez & Daniel F. Waggoner, 2025. "Uniform Priors for Impulse Responses," Econometrica, Econometric Society, vol. 93(2), pages 695-718, March.
    2. Atsushi Inoue & Lutz Kilian, 2020. "The Role of the Prior in Estimating VAR Models with Sign Restrictions," Working Papers 2030, Federal Reserve Bank of Dallas.
    3. 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.
    4. 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.
    5. Inoue, Atsushi & Kilian, Lutz, 2022. "Joint Bayesian inference about impulse responses in VAR models," Journal of Econometrics, Elsevier, vol. 231(2), pages 457-476.
    6. Thomas F. P. Wiesen & Paul M. Beaumont, 2024. "A joint impulse response function for vector autoregressive models," Empirical Economics, Springer, vol. 66(4), pages 1553-1585, April.
    7. repec:diw:diwwpp:dp1762 is not listed on IDEAS
    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. Inoue, Atsushi & Kilian, Lutz, 2020. "The uniform validity of impulse response inference in autoregressions," Journal of Econometrics, Elsevier, vol. 215(2), pages 450-472.
    10. Yambolov, Andrian, 2025. "How to conduct joint Bayesian inference in VAR models?," Working Paper Series 3100, European Central Bank.

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    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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