用D-vine SCAR模型模拟高维时变相关
Modeling high dimensional time-varying dependence using D-vine SCAR models
摘要：
我们考虑了多个时间序列之间相关性的建模问题。我们建立了高维时变copula模型，通过结合配对copula结构（PCC）与随机自回归copula（SCAR）模型来捕捉随时间变化的依赖关系。我们展示了如何这个高度复杂的模型的估计可以分解成一个序列的二元SCAR模型，这可以通过使用模拟的极大似然的方法来实现的估计。此外，通过将PCC的较高级联上的条件依赖参数限制为常数，我们可以大大减少要估计的参数的数量，而不会损失太多的灵活性。我们通过大规模的蒙特卡罗模拟研究了我们的估计方法的性能。一个大型数据集的股票收益的所有成分的达克斯30的应用程序说明了所提出的模型类的有用性。
英文摘要：
We consider the problem of modeling the dependence among many time series. We build high dimensional time-varying copula models by combining pair-copula constructions (PCC) with stochastic autoregressive copula (SCAR) models to capture dependence that changes over time. We show how the estimation of this highly complex model can be broken down into the estimation of a sequence of bivariate SCAR models, which can be achieved by using the method of simulated maximum likelihood. Further, by restricting the conditional dependence parameter on higher cascades of the PCC to be constant, we can greatly reduce the number of parameters to be estimated without losing much flexibility. We study the performance of our estimation method by a large scale Monte Carlo simulation. An application to a large dataset of stock returns of all constituents of the Dax 30 illustrates the usefulness of the proposed model class.
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