Multivariate distributions that allow for asymmetry and heavy tails are important building blocks in many econometric and statistical models. The Unified Skew-t (UST) is a promising choice because it is both scalable and allows for a high level of flexibility in the asymmetry in the distribution. However, it suffers from parameter identification and computational hurdles that have to date inhibited its use for modeling data. In this paper we propose a new tractable variant of the unified skew-t (TrUST) distribution that addresses both challenges. Moreover, the copula of this distribution is shown to also be tractable, while allowing for greater heterogeneity in asymmetric dependence over variable pairs than the popular skew-t copula. We show how Bayesian posterior inference for both the distribution and its copula can be computed using an extended likelihood derived from a generative representation of the distribution. The efficacy of this Bayesian method, and the enhanced flexibility of both the TrUST distribution and its implicit copula, is first demonstrated using simulated data. Applications of the TrUST distribution to highly skewed regional Australian electricity prices, and the TrUST copula to intraday U.S. equity returns, demonstrate how our proposed distribution and its copula can provide substantial increases in accuracy over the popular skew-t and its copula in practice.

翻译：允许不对称和厚尾的多元分布是许多计量经济学和统计模型的重要组成部分。统一偏斜-t分布（UST）因兼具可扩展性和分布不对称性的高度灵活性而成为一个有前景的选择。然而，它存在参数识别和计算难题，至今阻碍了其在数据建模中的应用。本文提出一种新的易处理统一偏斜-t变体（TrUST）分布，同时解决了上述两个挑战。此外，该分布的Copula也被证明是易处理的，且相较于流行的偏斜-t Copula，允许变量对间存在更大的非对称依赖异质性。我们展示了如何利用从该分布生成表示推导出的扩展似然，计算分布及其Copula的贝叶斯后验推断。首先通过模拟数据验证了该贝叶斯方法的有效性，以及TrUST分布及其隐式Copula增强的灵活性。将TrUST分布应用于高度偏斜的澳大利亚地区电价，并将TrUST Copula应用于美国日内股票收益，证明了我们提出的分布及其Copula在实践中相较于流行的偏斜-t及其Copula能够显著提高精度。