Bayesian Estimation of R-Vine Copula with Gaussian-Mixture GARCH Margins: An MCMC and Machine Learning Comparison

Khanthaporn, RewatWichitaksorn, Nuttanan2025-12-102025-12-102025-12-04Mathematics, ISSN: 2227-7390 (Print); 2227-7390 (Online), MDPI AG, 13(23), 3886-3886. doi: 10.3390/math132338862227-73902227-7390http://hdl.handle.net/10292/20393This study proposes Bayesian estimation of multivariate regular vine (R-vine) copula models with generalized autoregressive conditional heteroskedasticity (GARCH) margins modeled by Gaussian-mixture distributions. The Bayesian estimation approach includes Markov chain Monte Carlo and variational Bayes with data augmentation. Although R-vines typically involve computationally intensive procedures limiting their practical use, we address this challenge through parallel computing techniques. To demonstrate our approach, we employ thirteen bivariate copula families within an R-vine pair-copula construction, applied to a large number of marginal distributions. The margins are modeled as exponential-type GARCH processes with intertemporal capital asset pricing specifications, using a mixture of Gaussian and generalized Pareto distributions. Results from an empirical study involving 100 financial returns confirm the effectiveness of our approach.© 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).49 Mathematical Sciences4905 StatisticsBioengineeringregular vine copulasvariational bayes with data augmentationexponential-type generalised autoregressive conditional heteroskedasticity modelintertemporal capital asset pricing modelmixture distributionMarkov chain Monte CarloBayesian Estimation of R-Vine Copula with Gaussian-Mixture GARCH Margins: An MCMC and Machine Learning ComparisonJournal ArticleOpenAccess10.3390/math13233886