Large skew-t factor 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 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：大型偏斜t因子连接函数模型因其能够刻画非对称性和极端尾部依赖性，成为金融数据建模的吸引性选择。我们证明了Azzalini与Capitanio（2003）提出的偏斜t分布隐含的连接函数，相较于两种流行的替代偏斜t连接函数，可达到更高水平的成对非对称依赖。在高维场景下对此连接函数的估计极具挑战性，我们提出了一种快速且精确的贝叶斯变分推断方法来实现该估计。该方法利用偏斜t分布的条件高斯生成表示，定义了一个可被精确逼近的增广后验分布，并通过快速随机梯度上升算法求解变分优化问题。我们采用这一新方法，对2017年至2021年间93只美国股票的日内收益率进行了连接函数模型估计。结果表明，该连接函数不仅捕捉到了成对相关性的波动性，还揭示了股票对间非对称依赖性的显著异质性。我们进一步证明，基于偏斜t连接函数的日内预测密度优于其他若干连接函数模型，而基于估计的成对尾部依赖性的投资组合选择策略，相对于基准指数而言，其绩效表现更优。