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Approximation Properties of Variational Bayes for Vector Autoregressions

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  • Reza Hajargasht

Abstract

Variational Bayes (VB) is a recent approximate method for Bayesian inference. It has the merit of being a fast and scalable alternative to Markov Chain Monte Carlo (MCMC) but its approximation error is often unknown. In this paper, we derive the approximation error of VB in terms of mean, mode, variance, predictive density and KL divergence for the linear Gaussian multi-equation regression. Our results indicate that VB approximates the posterior mean perfectly. Factors affecting the magnitude of underestimation in posterior variance and mode are revealed. Importantly, We demonstrate that VB estimates predictive densities accurately.

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  • Reza Hajargasht, 2019. "Approximation Properties of Variational Bayes for Vector Autoregressions," Papers 1903.00617, arXiv.org.
    • Handle: RePEc:arx:papers:1903.00617
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    References listed on IDEAS

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    1. Korobilis, Dimitris & Koop, Gary, 2018. "Variational Bayes inference in high-dimensional time-varying parameter models," Essex Finance Centre Working Papers 22665, University of Essex, Essex Business School.
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    4. G. Elliott & C. Granger & A. Timmermann (ed.), 2013. "Handbook of Economic Forecasting," Handbook of Economic Forecasting, Elsevier, edition 1, volume 2, number 2.
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