Empirical evidence for multivariate stock suggests that there are changes from asymptotic independence to asymptotic dependence and vice versa. Under asymptotic independence, the probability of joint extremes vanishes, whereas under asymptotic dependence, this probability remains positive. In this paper, we propose a dynamic model for bivariate extremes that allows for smooth transitions between regimes of asymptotic independence and asymptotic dependence. In doing so, we ignore the bulk of the distribution and only model the joint tail of interest. We propose a maximum-likelihood estimator for the model parameters and demonstrate its accuracy in simulations. An empirical application to losses on the CAC 40 and DAX 30 illustrates that our model provides a detailed description of changes in the extremal dependence structure. Furthermore, we show that our model issues adequate forecasts of systemic risk, as measured by CoVaR. Finally, we find some evidence that our CoVaR forecasts outperform those of a benchmark dynamic t-copula model.returns

中文翻译：

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建模随时间变化的尾部依存关系，并将其应用于系统性风险预测*

多元股票的经验证据表明，从渐进独立性到渐进依赖性有变化，反之亦然。在渐近独立性下，联合极端的可能性消失，而在渐近依赖性下，该可能性仍然为正。在本文中，我们为双变量极端提出了一个动态模型，该模型允许渐进独立性和渐进依赖性之间的平稳过渡。这样做时，我们将忽略大部分分布，而仅对感兴趣的联合尾部建模。我们为模型参数提出了一个最大似然估计器，并在仿真中证明了其准确性。对CAC 40和DAX 30上的损失的经验应用表明，我们的模型提供了对极端依赖结构变化的详细描述。此外，我们证明，我们的模型可以对CoVaR测得的系统性风险做出充分的预测。最后，我们发现一些证据表明我们的CoVaR预测优于基准动态t- copula模型。返回