{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27431",
  "author_total": 4,
  "authors": [
    {
      "name": "Nicolas Chopin"
    },
    {
      "name": "Andras Fulop"
    },
    {
      "name": "Yuedan Huo"
    },
    {
      "name": "Anna Simoni"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bne3v2wa3gem2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27431",
  "fulltext_url": null,
  "id": "bne3v2wa3gem2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27431",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Markov Chains and Monte Carlo Methods"
    ]
  ],
  "openalex": "W7214182970",
  "pdf_url": "https://arxiv.org/pdf/2609.27431",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bne3v2wa3gem2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:06Z",
      "native_id": "2609.27431",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27431"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.CO",
      "subfield": "statistics"
    }
  ],
  "title": "Bayesian inference, on-line forecasting and model choice for large VAR models with Cholesky stochastic volatility",
  "title_text": "Bayesian inference, on-line forecasting and model choice for large VAR models with Cholesky stochastic volatility",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:06Z",
  "url": "https://research.draconitic.com/paper/bne3v2wa3gem2",
  "venue": "arXiv",
  "versions": []
}