Template-Type: ReDIF-Paper 1.0
Author-Name: Ping Wu
Author-Name-First: Ping
Author-Name-Last: Wu
Author-Email: ping.wu@strath.ac.uk
Author-Workplace-Name: Department of Economics, University of Strathclyde
Author-Name: Gary Koop
Author-Name-First: Gary
Author-Name-Last: Koop
Author-Email: gary.koop@strath.ac.uk
Author-Workplace-Name: Department of Economics, University of Strathclyde
Title: Fast, Order-Invariant Bayesian Inference in VARs using the Eigendecomposition of the Error Covariance Matrix
Abstract: Bayesian inference in Vector Autoregressions (VARs) involves manipulating large
matrices which appear in the posterior (or conditional posterior) of the VAR coe-
cients. For large VARs, the computational time involved with these manipulations
becomes so large as to make 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 bur-
den. 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 de-
pendence. 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 
exibility while maintaining many of the benets of conjugacy. We exploit
this 
exibility in order 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.
Length:  pages
Creation-Date: 2022-11
Revision-Date: 
Publication-Status: 
File-URL: https://www.strath.ac.uk/media/1newwebsite/departmentsubject/economics/research/researchdiscussionpapers/2023/23-10.pdf
File-Format: Application/pdf
Number: 2310
Classification-JEL: 
Keywords: Eigendecomposition, order invariance, large vector autoregression
Handle: RePEc:str:wpaper:2310