Comment on Large Bayesian vector autoregressions with stochastic volatility and non-conjugate priors''

Fully Bayesian inference in a vector autoregression with stochastic volatility (VAR-SV) typically relies on simulations from a multi-step Markov chain Monte Carlo (MCMC) algorithm. Carriero et al. (2019) propose a new, faster, triangular'' algorithm (TA) to replace the systemwide algorithm (SWA) in the most time-consuming step of the VAR-SV's standard MCMC algorithm. This paper analytically shows that the TA and SWA generally sample from different distributions, thereby disproving a central claim of Carriero et al. (2019). Replacing the SWA with the TA thus results in an ad hoc change to the MCMC algorithm's transition kernel, leaving a priori unknown the formal relationship between the model's posterior and simulations from the MCMC algorithm using the TA. Published by Elsevier B.V.

Automated summary

This article introduces a method for fully Bayesian inference in the VAR-SV model and compares the different effects of using the triangular algorithm and the systemwide algorithm in the MCMC algorithm.