Fast, Order-Invariant Bayesian Inference in VARs Using the Eigendecomposition of the Error Covariance Matrix

Bibliographic Data

ID19420156
AuthorsPing Wu (0000-0002-0788-6268, University of Strathclyde), Wu Ping (0000-0001-6215-4847, University of Strathclyde, corresponding author), Gary Koop (0000-0002-6091-378X, University of Strathclyde)
Year2026
Pages1-13
Publication date2026-02-23
Open AccessYes
TypeARTICLE
VenueJournal of Business and Economic Statistics (JOURNAL)
Journal identifiersISSN: 0735-0015 • E-ISSN: 1537-2707
PublisherInforma UK Limited (PUBLISHER • GB)
DOI10.1080/07350015.2025.2560369
OpenAlexW4414153741
LanguageEN
References cited35

Bayesian inference in Vector Autoregressions (VARs) involves manipulating large matrices which appear in the posterior (or conditional posterior) of the VAR coefficients. For large VARs, the computational burden of these manipulations can render empirical work impractical. In response to this, many researchers transform their VARs so as to allow for Bayesian estimation to proceed one equation at a time. This leads to a massive reduction in the computational burden. This transformation involves taking the Cholesky decomposition for the error covariance matrix. However, this strategy implies that posterior inference depends on the order the variables enter the VAR. In this paper we develop an alternative transformation, based on the eigendecomposition, which does not lead to order dependence. Beginning with an inverse-Wishart prior on the error covariance matrix, we derive and discuss the properties of the prior it implies on the eigenmatrix and eigenvalues. We then show how an extension of the prior on the eigenmatrix can allow for greater flexibility while maintaining many of the benefits of conjugacy. We leverage this flexibility to extend the prior on the eigenvalues to allow for stochastic volatility. The properties of the eigendecomposition approach are investigated in a macroeconomic forecasting exercise involving VARs with 20 variables

Bayesian inference · Bayesian probability · Covariance · Covariance matrix · Inference · Fault Detection and Control Systems · Monetary Policy and Economic Impact · Probabilistic and Robust Engineering Design

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