Consistent Estimation of Multiple Breakpoints in Dependence Measures

This article proposes different methods to consistently detect multiple breaks in copula-based dependence measures. Starting with the classical binary segmentation, also the more recent wild binary segmentation (WBS) is considered. For binary segmentation, consistency of the estimators for the location of the breakpoints as well as the number of breaks is proved, taking filtering effects from AR-GARCH models explicitly into account. Monte Carlo simulations based on a factor copula as well as on a Clayton copula model illustrate the strengths and limitations of the procedures. A real data application on recent Euro Stoxx 50 data reveals some interpretable breaks in the dependence structure.本文提出了多种可一致检测基于连接函数（copula）的相依度量中多重变点的方法。本文以经典二元分割法为研究起点，同时考量了近年来提出的野生二元分割法（wild binary segmentation, WBS）。针对二元分割法，本文证明了变点位置估计量与变点个数估计量的一致性，并显式考虑了AR-GARCH模型的滤波效应。基于因子连接函数（factor copula）与Clayton连接函数（Clayton copula）的蒙特卡洛模拟，验证了所提流程的优势与局限性。针对近期欧元斯托克50指数（Euro Stoxx 50）的真实数据应用，揭示了相依结构中若干可解释的变点。