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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.

Suggested Citation

  • 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. Koop, Gary & Korobilis, Dimitris, 2010. "Bayesian Multivariate Time Series Methods for Empirical Macroeconomics," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(4), pages 267-358, July.
    2. Ormerod, J. T. & Wand, M. P., 2010. "Explaining Variational Approximations," The American Statistician, American Statistical Association, vol. 64(2), pages 140-153.
    3. 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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    Cited by:

    1. Ter Steege, Lucas, 2024. "Variational inference for Bayesian panel VAR models," Working Paper Series 2991, European Central Bank.

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