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Inference in VARs with Conditional Heteroskedasticity of Unknown Form

Author

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  • Ralf Brüggemann

    () (Department of Economics, University of Konstanz, Germany)

  • Carsten Jentsch

    () (Department of Economics, University of Mannheim, Germany)

  • Carsten Trenkler

    () (Department of Economics, University of Mannheim, Germany)

Abstract

We derive a framework for asymptotically valid inference in stable vector autoregressive (VAR) models with conditional heteroskedasticity of unknown form. We prove a joint central limit theorem for the VAR slope parameter and innovation covariance parameter estimators and address bootstrap inference as well. Our results are important for correct inference on VAR statistics that depend both on the VAR slope and the variance parameters as e.g. in structural impulse response functions (IRFs). We also show that wild and pairwise bootstrap schemes fail in the presence of conditional heteroskedasticity if inference on (functions) of the unconditional variance parameters is of interest because they do not correctly replicate the relevant fourth moments' structure of the error terms. In contrast, the residual-based moving block bootstrap results in asymptotically valid inference. We illustrate the practical implications of our theoretical results by providing simulation evidence on the finite sample properties of different inference methods for IRFs. Our results point out that estimation uncertainty may increase dramatically in the presence of conditional heteroskedasticity. Moreover, most inference methods are likely to understate the true estimation uncertainty substantially in finite samples.

Suggested Citation

  • Ralf Brüggemann & Carsten Jentsch & Carsten Trenkler, 2014. "Inference in VARs with Conditional Heteroskedasticity of Unknown Form," Working Paper Series of the Department of Economics, University of Konstanz 2014-13, Department of Economics, University of Konstanz.
  • Handle: RePEc:knz:dpteco:1413
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    References listed on IDEAS

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    Cited by:

    1. Lütkepohl, Helmut & Netšunajev, Aleksei, 2017. "Structural vector autoregressions with heteroskedasticity: A review of different volatility models," Econometrics and Statistics, Elsevier, vol. 1(C), pages 2-18.
    2. Inoue, Atsushi & Kilian, Lutz, 2016. "Joint confidence sets for structural impulse responses," Journal of Econometrics, Elsevier, vol. 192(2), pages 421-432.
    3. Lloyd, S. P., 2017. "Unconventional Monetary Policy and the Interest Rate Channel: Signalling and Portfolio Rebalancing," Cambridge Working Papers in Economics 1735, Faculty of Economics, University of Cambridge.
    4. Götz, Thomas B. & Hecq, Alain & Smeekes, Stephan, 2016. "Testing for Granger causality in large mixed-frequency VARs," Journal of Econometrics, Elsevier, vol. 193(2), pages 418-432.
    5. McCracken, Michael W. & McGillicuddy, Joseph, 2017. "An Empirical Investigation of Direct and Iterated Multistep Conditional Forecasts," Working Papers 2017-40, Federal Reserve Bank of St. Louis.
    6. Lunsford, Kurt Graden, 2015. "Identifying Structural VARs with a Proxy Variable and a Test for a Weak Proxy," Working Paper 1528, Federal Reserve Bank of Cleveland.
    7. Lutz Kilian & Xiaoqing Zhou, 2018. "The Propagation of Regional Shocks in Housing Markets: Evidence from Oil Price Shocks in Canada," CESifo Working Paper Series 7005, CESifo Group Munich.
    8. Enzo Weber & Roland Weigand, 2018. "Identifying macroeconomic effects of refugee migration to Germany," Economics Bulletin, AccessEcon, vol. 38(2), pages 852-862.
    9. Stefan Bruder, 2018. "Inference for structural impulse responses in SVAR-GARCH models," ECON - Working Papers 281, Department of Economics - University of Zurich.
    10. Brüggemann, Ralf & Jentsch, Carsten & Trenkler, Carsten, 2016. "Inference in VARs with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 191(1), pages 69-85.
    11. Michele Piffer & Maximilian Podstawski, 2017. "Identifying Uncertainty Shocks Using the Price of Gold," CESifo Working Paper Series 6327, CESifo Group Munich.
    12. repec:eee:dyncon:v:84:y:2017:i:c:p:43-57 is not listed on IDEAS
    13. Jentsch, Carsten & Lunsford, Kurt G., 2016. "Proxy SVARs : asymptotic theory, bootstrap inference, and the effects of income tax changes in the United States," Working Papers 16-10, University of Mannheim, Department of Economics.
    14. Michele Piffer & Maximilian Podstawski, 2016. "Identifying Uncertainty Shocks Using the Price of Gold," Discussion Papers of DIW Berlin 1549, DIW Berlin, German Institute for Economic Research.
    15. Clark, Todd E. & McCracken, Michael W., 2014. "Evaluating Conditional Forecasts from Vector Autoregressions," Working Paper 1413, Federal Reserve Bank of Cleveland.
    16. Dominik Bertsche & Robin Braun, 2017. "Identification of Structural Vector Autoregressions by Stochastic Volatility," Working Paper Series of the Department of Economics, University of Konstanz 2017-11, Department of Economics, University of Konstanz.
    17. Helmut Lütkepohl & Thore Schlaak, 2018. "Bootstrapping Impulse Responses of Structural Vector Autoregressive Models Identified through GARCH," Discussion Papers of DIW Berlin 1750, DIW Berlin, German Institute for Economic Research.
    18. Christoph Große Steffen & Maximilian Podstawski, 2016. "Ambiguity and Time-Varying Risk Aversion in Sovereign Debt Markets," Discussion Papers of DIW Berlin 1602, DIW Berlin, German Institute for Economic Research.
    19. Zhu, Ke & Li, Wai Keung, 2015. "A bootstrapped spectral test for adequacy in weak ARMA models," Journal of Econometrics, Elsevier, vol. 187(1), pages 113-130.
    20. Lenard Lieb & Stephan Smeekes, 2017. "Inference for Impulse Responses under Model Uncertainty," Papers 1709.09583, arXiv.org, revised May 2018.
    21. repec:spr:stpapr:v:58:y:2017:i:4:d:10.1007_s00362-016-0744-0 is not listed on IDEAS
    22. G. Angelini & L. Fanelli, 2018. "Identification and estimation issues in Structural Vector Autoregressions with external instruments," Working Papers wp1122, Dipartimento Scienze Economiche, Universita' di Bologna.

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    Keywords

    VAR; Conditional heteroskedasticity; Residual-based moving block bootstrap; Pairwise bootstrap; Wild bootstrap;

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • 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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