Bayesian inference, on-line forecasting and model choice for large VAR models with Cholesky stochastic volatility
Abstract
We consider K-dimensional Bayesian vector autoregressions (BVARs) with Cholesky stochastic volatility (SV), in which the innovation covariance matrix is a lower-triangular linear transform of K independent univariate SV processes. Such models are widely used in empirical macroeconomics to capture time-varying uncertainty and improve forecast accuracy, but the cost of posterior simulation is the binding constraint on the size of the system, and a major bottleneck for empirical work. We introduce a Markov chain Monte Carlo (MCMC) kernel that mixes better than existing samplers at the same computational complexity. It rests on a reparametrisation that makes the K volatility trajectories conditionally independent, and on Particle Gibbs to update each trajectory. The kernel targets the exact posterior, rather than an approximation of it, and in an application with K = 15 it raises the mean effective sample size per second, relative to the benchmark corrected triangular algorithm, by a factor of approximately $14$ for the VAR coefficients and $3.4$ for the volatilities. We also introduce a a Sequential Monte Carlo squared (\smcsq{}) sampler, which used our MCMC kernel as a building block, and which delivers at every t the one-step-ahead predictive density and the marginal likelihood of the data up to t, and hence on-line forecasting and model choice. To our knowledge, this is the first algorithm that delivers sequential marginal likelihoods for Cholesky-SV BVARs with static contemporaneous coefficients and a non-conjugate prior. We illustrate both on US monthly macroeconomic data, with K=15 for posterior inference and K=6 for the sequential sampler and model choice.
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BibTeX
@misc{chopin2026bayesian,
title = {{Bayesian inference, on-line forecasting and model choice for large VAR models with Cholesky stochastic volatility}},
author = {Nicolas Chopin and Andras Fulop and Yuedan Huo and Anna Simoni},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27431},
eprint = {2609.27431},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27431},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bayesian inference, on-line forecasting and model choice for large VAR models with Cholesky stochastic volatility
AU - Nicolas Chopin
AU - Andras Fulop
AU - Yuedan Huo
AU - Anna Simoni
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27431
UR - https://arxiv.org/abs/2609.27431
AB - We consider K-dimensional Bayesian vector autoregressions (BVARs) with Cholesky stochastic volatility (SV), in which the innovation covariance matrix is a lower-triangular linear transform of K independent univariate SV processes. Such models are widely used in empirical macroeconomics to capture time-varying uncertainty and improve forecast accuracy, but the cost of posterior simulation is the binding constraint on the size of the system, and a major bottleneck for empirical work. We introduce a Markov chain Monte Carlo (MCMC) kernel that mixes better than existing samplers at the same computational complexity. It rests on a reparametrisation that makes the K volatility trajectories conditionally independent, and on Particle Gibbs to update each trajectory. The kernel targets the exact posterior, rather than an approximation of it, and in an application with K = 15 it raises the mean effective sample size per second, relative to the benchmark corrected triangular algorithm, by a factor of approximately $14$ for the VAR coefficients and $3.4$ for the volatilities. We also introduce a a Sequential Monte Carlo squared (\smcsq{}) sampler, which used our MCMC kernel as a building block, and which delivers at every t the one-step-ahead predictive density and the marginal likelihood of the data up to t, and hence on-line forecasting and model choice. To our knowledge, this is the first algorithm that delivers sequential marginal likelihoods for Cholesky-SV BVARs with static contemporaneous coefficients and a non-conjugate prior. We illustrate both on US monthly macroeconomic data, with K=15 for posterior inference and K=6 for the sequential sampler and model choice.
ER -