Two-Sample Testing for Tail Copulas with an Application to Equity Indices

A novel, general two-sample hypothesis testing procedure is established for testing the equality of tail copulas associated with bivariate data. More precisely, using a martingale transformation of a natural two-sample tail copula process, a test process is constructed, which is shown to converge in distribution to a standard Wiener process. Hence, from this test process a myriad of asymptotically distribution-free two-sample tests can be obtained. The good finite-sample behavior of our procedure is demonstrated through Monte Carlo simulations. Using the new testing procedure, no evidence of a difference in the respective tail copulas is found for pairs of negative daily log-returns of equity indices during and after the global financial crisis.

本研究确立了一种新颖的、通用的双样本假设检验程序，用于检验与二元数据相关的尾部 Copula 的等价性。更确切地说，通过自然双样本尾部 Copula 过程的鞅变换，构建了一个检验过程，并证明其在分布上收敛于标准维纳过程。因此，基于此检验过程，可以衍生出众多渐近分布自由的双样本检验。通过蒙特卡洛模拟，展示了该程序在有限样本下的优良性能。运用新的检验程序，发现在全球金融危机期间及之后，股票指数负对数日回报率对之间的尾部 Copula 没有发现显著差异。