Inference in VARs with Conditional Heteroskedasticity of Unknown Form

Ralf Brüggemann, Carsten Jentsch and Carsten Trenkler

No 14-21, Working Papers from University of Mannheim, Department of Economics

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.

Keywords: VAR; Conditional heteroskedasticity; Residual-based moving block bootstrap; Pairwise bootstrap; Wild bootstrap (search for similar items in EconPapers)
JEL-codes: C30 C32 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (16)

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Related works:
Journal Article: Inference in VARs with conditional heteroskedasticity of unknown form (2016)
Working Paper: Inference in VARs with Conditional Heteroskedasticity of Unknown Form (2014)
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