Skew-t copula models are attractive for the modeling of financial data because they allow for asymmetric and extreme tail dependence. We show that the copula implicit in the skew-t distribution of Azzalini and Capitanio (2003) allows for a higher level of pairwise asymmetric dependence than two popular alternative skew-t copulas. Estimation of this copula in high dimensions is challenging, and we propose a fast and accurate Bayesian variational inference (VI) approach to do so. The method uses a conditionally Gaussian generative representation of the skew-t distribution to define an augmented posterior that can be approximated accurately. A fast stochastic gradient ascent algorithm is used to solve the variational optimization. The new methodology is used to estimate skew-t factor copula models for intraday returns from 2017 to 2021 on 93 U.S. equities. The copula captures substantial heterogeneity in asymmetric dependence over equity pairs, in addition to the variability in pairwise correlations. We show that intraday predictive densities from the skew-t copula are more accurate than from some other copula models, while portfolio selection strategies based on the estimated pairwise tail dependencies improve performance relative to the benchmark index.

翻译：偏t Copula模型因其能够捕捉非对称和极端尾部相依性，在金融数据建模中具有显著优势。我们证明，Azzalini与Capitanio（2003）提出的偏t分布所隐含的Copula，能比两种常见的替代偏t Copula实现更高水平的成对非对称相依性。高维情形下该Copula的估计颇具挑战性，为此我们提出一种快速且准确的贝叶斯变分推断方法。该方法利用偏t分布的条件高斯生成表示定义增广后验分布，从而可实现高精度近似；并采用快速随机梯度上升算法求解变分优化问题。我们运用该新方法，基于2017至2021年间93只美国股票的日内收益数据，估计了偏t因子Copula模型。该Copula不仅揭示了成对相关系数的变异性，更捕获了股票对间非对称相依性的显著异质性。研究表明，基于偏t Copula的日内预测密度优于其他Copula模型，而利用估计的成对尾部相依性构建的投资组合策略，其表现也优于基准指数。