In this article, we propose a class of multivariate non‐Gaussian time series models which include dynamic versions of many well‐known distributions and consider their Bayesian analysis. A key feature of our proposed model is its ability to account for correlations across time as well as across series (contemporary) via a common random environment. The proposed modeling approach yields analytically tractable dynamic marginal likelihoods, a property not typically found outside of linear Gaussian time series models. These dynamic marginal likelihoods can be tied back to known static multivariate distributions such as the Lomax, generalized Lomax, and the multivariate Burr distributions. The availability of the marginal likelihoods allows us to develop efficient estimation methods for various settings using Markov chain Monte Carlo as well as sequential Monte Carlo methods. Our approach can be considered to be a multivariate generalization of commonly used univariate non‐Gaussian class of state space models. To illustrate our methodology, we use simulated data examples and a real application of multivariate time series for modeling the joint dynamics of stochastic volatility in financial indexes, the VIX and VXN.
