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Inference in VARs with Conditional Heteroskedasticity of Unknown Form

Author

Listed:
  • 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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    More about this item

    Keywords

    VAR; Conditional heteroskedasticity; Residual-based moving block bootstrap; Pairwise bootstrap; Wild bootstrap;
    All these keywords.

    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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