We introduce a novel model for time-varying, asymmetric, tail-dependent copulas in high dimensions that incorporates both spectral dynamics and regularization. The dynamics of the dependence matrix' eigenvalues are modeled in a score-driven way, while biases in the unconditional eigenvalue spectrum are resolved by non-linear shrinkage. The dynamic parameterization of the copula dependence matrix ensures that it satisfies the appropriate restrictions at all times and for any dimension. The model is parsimonious, computationally efficient, easily scalable to high dimensions, and performs well for both simulated and empirical data. In an empirical application to financial market dynamics using 100 stocks from 10 different countries and 10 different industry sectors, we find that our copula model captures both geographic and industry related co-movements and outperforms recent computationally more intensive clustering-based factor copula alternatives. Both the spectral dynamics and the regularization contribute to the new model's performance. During periods of market stress, we find that the spectral dynamics reveal strong increases in international stock market dependence, which causes reductions in diversification potential and increases in systemic risk.

翻译：本文提出了一种新颖的时变、非对称、尾部相依的高维Copula模型，该模型同时融合了谱动力学与正则化机制。我们采用分数驱动方式对相依矩阵特征值的动态变化进行建模，并通过非线性收缩方法解决无条件特征值谱中的偏差问题。Copula相依矩阵的动态参数化确保其在任意时刻及任意维度下均满足相应的约束条件。该模型具有参数简约、计算高效、易于扩展至高维的特点，并在模拟数据与实证数据中均表现优异。在一项针对金融市场的实证应用中，我们选取了来自10个不同国家、10个不同行业的100支股票数据，发现本文提出的Copula模型能够有效捕捉地理与行业层面的联动效应，其表现优于近期计算复杂度更高的基于聚类的因子Copula替代模型。谱动力学与正则化机制共同提升了新模型的性能。在市场压力时期，谱动力学分析显示国际股票市场相依性显著增强，导致分散化投资潜力下降，系统性风险上升。