Bernardi, MauroBianchi, DanieleBianco, Nicolas2025-03-182025-03-182024Bernardi M, Bianchi D, Bianco N. Variational inference for large Bayesian vector autoregressions. J Bus Econ Stat. 2024;42(3):1066-82. DOI: 10.1080/07350015.2023.22907160735-0015http://hdl.handle.net/10230/69951We propose a novel variational Bayes approach to estimate high-dimensional Vector Autoregressive (VAR) models with hierarchical shrinkage priors. Our approach does not rely on a conventional structural representation of the parameter space for posterior inference. Instead, we elicit hierarchical shrinkage priors directly on the matrix of regression coefficients so that (a) the prior structure maps into posterior inference on the reduced-form transition matrix and (b) posterior estimates are more robust to variables permutation. An extensive simulation study provides evidence that our approach compares favorably against existing linear and nonlinear Markov chain Monte Carlo and variational Bayes methods. We investigate the statistical and economic value of the forecasts from our variational inference approach for a mean-variance investor allocating her wealth to different industry portfolios. The results show that more accurate estimates translate into substantial out-of-sample gains across hierarchical shrinkage priors and model dimensions.application/pdfeng© 2024 The Authors. Published with license by Taylor & Francis Group, LLC.This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), whichpermits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way. The terms onwhich this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent.info:eu-repo/semantics/articlehttp://dx.doi.org/10.1080/07350015.2023.2290716Bayesian methodsHierarchical shrinkage priorHigh-dimensional modelsIndustry returns predictabilityVariational inferenceVector autoregressionsinfo:eu-repo/semantics/openAccess