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 generative representation of the skew-t distribution to define an augmented posterior that can be approximated accurately. A stochastic gradient ascent algorithm is used to solve the variational optimization. The methodology is used to estimate skew-t factor copula models with up to 15 factors 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. In a moving window study we show that the asymmetric dependencies also vary over time, and that intraday predictive densities from the skew-t copula are more accurate than those from benchmark copula models. Portfolio selection strategies based on the estimated pairwise asymmetric dependencies improve performance relative to the index.

翻译：偏斜t-藤模型因其能够刻画非对称与极端尾部依赖性，在金融数据建模中颇具吸引力。本文证明，Azzalini与Capitanio（2003）提出的偏斜t分布所隐含的藤模型，相较于两种常用的替代偏斜t-藤模型，能够刻画更高程度的成对非对称依赖性。该藤模型在高维情形下的估计具有挑战性，为此我们提出一种快速且准确的贝叶斯变分推断方法。该方法利用偏斜t分布的生成表示来定义一个可被精确逼近的增广后验分布，并采用随机梯度上升算法求解变分优化问题。我们将该方法论应用于2017年至2021年间93只美国股票日内收益的建模，估计了包含多达15个因子的偏斜t因子藤模型。该藤模型不仅捕捉了成对相关性之间的差异性，还揭示了不同股票对之间非对称依赖性的显著异质性。通过滚动窗口研究，我们发现非对称依赖性亦随时间变化，且基于偏斜t-藤模型的日内预测密度比基准藤模型更为准确。基于估计所得成对非对称依赖性的投资组合选择策略，相较于基准指数表现出更优的绩效。