Asymptotically valid Bayesian inference in the presence of distributional misspecification in VAR models

Katerina Petrova

Journal of Econometrics, 2022, vol. 230, issue 1, 154-182

Abstract: Inaccurately imposing Gaussian distributional assumptions in standard multivariate time series models does not affect inference on the autoregressive coefficients but distorts both classical and Bayesian inference on the volatility matrix whenever the true error distribution has excess kurtosis relative to the multivariate normal density. Inference on the intercept is also affected whenever the innovations are generated from a non-symmetric distribution. As a result of distributional misspecification, Bayesian methods lead to asymptotically invalid posterior inference for the intercept and the volatility matrix and, consequently, invalid posterior credible sets for quantities such as impulse responses, variance decompositions and density forecasts. We propose a robust and computationally fast Bayesian procedure which delivers asymptotically correct posterior credible sets without the need for distributional assumptions. The proposed corrected Bayesian posteriors for the volatility matrix and the intercept vector are based on the asymptotic covariance of the QML estimators and admit a closed form. Implementation of the procedure requires consistent estimation of the multivariate skewness and kurtosis of the innovations, and we propose novel shrinkage estimators designed to shrink these large dimensional objects towards the skewness and kurtosis of a Gaussian vector. We extend our robust Bayesian analysis to accommodate non-Gaussian disturbances in the presence of parameter instability, by combining the estimators of the current paper with semi-parametric kernel-type methods. We demonstrate that our estimators deliver correct posterior coverage rates in an extensive Monte Carlo exercise under a variety of distributional specifications. Finally, we present empirical evidence that imposing Gaussianity or homoskedasticity assumptions on financial and uncertainty shocks is not justified and may lead to misleading empirical conclusions.

Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304407621000865
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:230:y:2022:i:1:p:154-182

DOI: 10.1016/j.jeconom.2020.12.011

Access Statistics for this article

Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

More articles in Journal of Econometrics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().