Inference in VARs with Conditional Heteroskedasticity of Unknown Form


Brüggemann, Ralf ; Jentsch, Carsten ; Trenkler, Carsten


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URL: https://ub-madoc.bib.uni-mannheim.de/36858
URN: urn:nbn:de:bsz:180-madoc-368583
Document Type: Working paper
Year of publication: 2014
The title of a journal, publication series: Working Paper Series
Volume: 14-21
Place of publication: Mannheim
Publication language: English
Institution: School of Law and Economics > VWL, Empirische Wirtschaftsforschung (Trenkler)
MADOC publication series: Department of Economics > Working Paper Series
Subject: 330 Economics
Classification: JEL: C30 , C32,
Keywords (English): VAR , Conditional heteroskedasticity , Residual-based moving block bootstrap , Pairwise bootstrap , Wild bootstrap
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.

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