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Comparison of methods for constructing joint confidence bands for impulse response functions

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

Abstract

In vector autoregressive analyses, confidence intervals for individual impulse responses are typically reported in order to indicate the sampling uncertainty in the estimation results. Various methods are reviewed, and a new method for the construction of joint confidence bands, given a prespecified coverage level, for the impulse responses at all horizons considered simultaneously, is proposed. The methods are compared in a simulation experiment, and recommendations for empirical work are provided.

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  • Lütkepohl, Helmut & Staszewska-Bystrova, Anna & Winker, Peter, 2015. "Comparison of methods for constructing joint confidence bands for impulse response functions," International Journal of Forecasting, Elsevier, vol. 31(3), pages 782-798.
  • Handle: RePEc:eee:intfor:v:31:y:2015:i:3:p:782-798
    DOI: 10.1016/j.ijforecast.2013.08.003
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    Cited by:

    1. Boer, Lukas & Lütkepohl, Helmut, 2021. "Qualitative versus quantitative external information for proxy vector autoregressive analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).
    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. 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.
    4. Yanwei Zhang & Hualin Xie, 2019. "Interactive Relationship among Urban Expansion, Economic Development, and Population Growth since the Reform and Opening up in China: An Analysis Based on a Vector Error Correction Model," Land, MDPI, Open Access Journal, vol. 8(10), pages 1-31, October.
    5. 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.
    6. Inoue, Atsushi & Kilian, Lutz, 2016. "Joint confidence sets for structural impulse responses," Journal of Econometrics, Elsevier, vol. 192(2), pages 421-432.
    7. Lütkepohl, Helmut & Schlaak, Thore, 2019. "Bootstrapping impulse responses of structural vector autoregressive models identified through GARCH," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 41-61.
    8. Walentin, Karl, 2014. "Business cycle implications of mortgage spreads," Journal of Monetary Economics, Elsevier, vol. 67(C), pages 62-77.
    9. 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.
    10. 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.
    11. Poeschel, Friedrich, 2012. "Assortative matching through signals," VfS Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62061, Verein für Socialpolitik / German Economic Association.
    12. Inoue, Atsushi & Kilian, Lutz, 2020. "Joint Bayesian inference about impulse responses in VAR models," CFS Working Paper Series 650, Center for Financial Studies (CFS).
    13. 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.
    14. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2018. "Estimation of structural impulse responses: short-run versus long-run identifying restrictions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 229-244, April.
    15. 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.
    16. 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.
    17. Inoue, Atsushi & Kilian, Lutz, 2020. "The uniform validity of impulse response inference in autoregressions," Journal of Econometrics, Elsevier, vol. 215(2), pages 450-472.
    18. Jørgen Bølstad & Christoph Elhardt, 2015. "To bail out or not to bail out? Crisis politics, credibility, and default risk in the Eurozone," European Union Politics, , vol. 16(3), pages 325-346, September.
    19. Schüssler, Rainer & Trede, Mark, 2016. "Constructing minimum-width confidence bands," Economics Letters, Elsevier, vol. 145(C), pages 182-185.
    20. Martin Bruns & Helmut Lütkepohl, 2020. "An Alternative Bootstrap for Proxy Vector Autoregressions," Discussion Papers of DIW Berlin 1913, DIW Berlin, German Institute for Economic Research.
    21. Martin Bruns & Helmut Lütkepohl, 2021. "Comparison of Local Projection Estimators for Proxy Vector Autoregressions," Discussion Papers of DIW Berlin 1949, DIW Berlin, German Institute for Economic Research.
    22. Lenard Lieb & Stephan Smeekes, 2017. "Inference for Impulse Responses under Model Uncertainty," Papers 1709.09583, arXiv.org, revised Oct 2019.
    23. Grabowski Daniel & Winker Peter & Staszewska-Bystrova Anna, 2017. "Generating prediction bands for path forecasts from SETAR models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(5), pages 1-18, December.
    24. Niklas Ahlgren & Paul Catani, 2017. "Wild bootstrap tests for autocorrelation in vector autoregressive models," Statistical Papers, Springer, vol. 58(4), pages 1189-1216, December.
    25. Adam Kuèera & Evžen Koèenda & Aleš Maršál, 2019. "Yield Curve Dynamics and Fiscal Policy Shocks," Working and Discussion Papers WP 2/2019, Research Department, National Bank of Slovakia.

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    More about this item

    Keywords

    Vector autoregressive process; Impulse responses; Bootstrap; Confidence band;
    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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