Title: Bayesian inference for dynamic vine copulas in higher dimensions Show Chinese title

Title: 高维动态藤copula的贝叶斯推理

Abstract: We propose a class of dynamic vine copula models. This is an extension of static vine copulas and a generalization of dynamic C-vine and D-vine copulas studied by Almeida et al (2016) and Goel and Mehra (2019). Within this class, we allow for time-varying dependence by driving the vine copula parameters with latent AR(1) processes. This modeling approach is very flexible but estimation is not straightforward due to the high-dimensional parameter space. We propose a Bayesian estimation approach, which relies on a novel approximation of the posterior distribution. This approximation allows to use Markov Chain Monte Carlo methods, such as elliptical slice sampling, in a sequential way. In contrast to other Bayesian sequential estimation procedures for vine copula models as proposed by Gruber and Czado (2015), there is no need to collapse copula parameters to point estimates before proceeding to the next tree. Thus more information and uncertainty is propagated from lower to higher trees. A simulation study shows satisfactory performance of the Bayesian procedure. This dynamic modeling and inference approach can be applied in various fields, where static vine copulas have already proven to be successful, including environmental sciences, medicine and finance. Here we study the dependence among 21 exchange rates. For comparison we also estimate a static vine copula model and dynamic C-vine and D-vine copula models. This comparison shows superior performance of the proposed dynamic vine copula model with respect to one day ahead forecasting accuracy. Show Chinese abstract

Abstract: 我们提出了一类动态藤 Copula 模型。 这是静态藤 Copula 的扩展，并且是对 Almeida 等人（2016年）以及 Goel 和 Mehra（2019年）研究的动态 C-藤和 D-藤 Copula 的推广。 在这一类别中，我们通过使用潜在的 AR(1) 过程驱动藤 Copula 参数来允许时间变化的依赖性。 这种建模方法非常灵活，但由于高维参数空间，估计并不简单。 我们提出了一种贝叶斯估计方法，该方法依赖于后验分布的一种新近似。 这种近似允许以序列方式使用马尔可夫链蒙特卡洛方法，例如椭圆切片抽样。 与 Gruber 和 Czado（2015年）提出的其他贝叶斯顺序估计程序不同，在进入下一棵树之前无需将 Copula 参数缩减为点估计。 因此，更多信息和不确定性从较低的树传播到较高的树。 模拟研究表明了贝叶斯过程令人满意的性能。 这种动态建模和推理方法可以应用于静态藤 Copula 已经证明成功的各个领域，包括环境科学、医学和金融。 在这里，我们研究了21种汇率之间的依赖关系。 为了比较，我们还估计了一个静态藤 Copula 模型和动态 C-藤和 D-藤 Copula 模型。 这种比较显示了所提出的动态藤 Copula 模型在一天前预测准确性方面的优越性能。