Beyond Dimension two: A Test for Higher-Order Tail Risk
提出一种检验方法，用于检测当尾部风险的多元依赖结构存在高于二维的维度时，传统的两两比较方法是否失效，并通过模拟和实际股票指数数据验证其有效性。
In practice, multivariate dependencies between extreme risks are often only assessed in a pairwise way. We propose a test for detecting situations when such pairwise measures are inadequate and give incomplete results. This occurs when a significant portion of the multivariate dependence structure in the tails is of higher dimension than 2. Our test statistic is based on a decomposition of the stable tail dependence function describing multivariate tail dependence. The asymptotic properties of the test are provided and a bootstrap-based finite sample version of the test is proposed. A simulation study documents good size and power properties of the test including settings with time-series components and factor models. In an application to stock indices for non-crisis times, pairwise tail models seem appropriate for global markets while the test finds them not admissible for the tightly interconnected European market. From 2007/2008 on, however, higher order dependencies generally increase and require a multivariate tail model in all cases.