SGER: Statistics of Extremes, with Applications in Financial Time Series

该提案追求尾部独立性的新测试统计量和尾部依赖性的新措施的一系列发展。特别地，研究者研究了极端相关系数、尾部依赖度量、伽玛检验统计量。这些都与多元极值的统计研究有关。在金融应用方面，该提案还将为资产定价和市场数据的极端联合运动指定新的模型，并开发对这些生态运动更敏感的新的投资组合评估工具。介绍了一种新的极端联合运动测量方法。该建议包括发展最大稳定过程的统计估计方法。如何计算投资组合风险措施的程序也介绍了使用组合马尔可夫过程和最大稳定过程模型。由于用于极值依赖性的所有定义都依赖于一些极限过程，并且通常涉及对特定参数空间边缘的参数进行统计检验，因此必须非常小心地获得具有足够功率的检验。这个提议的目的就是要找到解决这个问题的办法。研究者将使用模拟和真实数据仔细比较和对比新方法与现有方法。真实的数据将来自不同的领域，如保险、金融、电信、气候学、地震学、医学等。在各个领域（如上所述）的应用中，极端风险扮演着重要的科学、社会以及（可能）政治角色。新统计工具的传播有助于更好地理解联合极值的发生，这是非常重要的。这可以在新研究生课程、面向广泛读者的期刊上的出版物以及与其他领域的科学家的讨论中很好地实现。

The proposal pursues a series of developments of new test statisticsfor tail independence and of new measures for tail dependence.Particularly, the investigator studies extreme correlationcoefficient, tail dependence measures, gamma test statistics. Theseare related to the study of statistics of multivariate extremes. Infinancial applications, the proposal will also specify new modelsfor asset pricing and extreme co-movements for market data, anddevelop new portfolio evaluation tools more sensitive to theseco-movements. A new measure for extreme co-movement is introduced.The proposal includes the development of statistical estimationmethods for max-stable processes. Procedures of how to calculateportfolio risk measures are also introduced using combined Markovprocess and max-stable process models.As all definitions used for extremal dependence depend on some limitprocedures and often concern statistical testing for parameters atthe edge of a specific parametric space, great care has to be takento obtain tests with sufficient power. The proposal is exactlyaiming at finding a solution for this. The investigator willcarefully compare and contrast new approaches with existing onesusing simulated as well as real data. The real data will come fromareas as diverse as insurance, finance, telecommunications,climatology, seismology, medicine, etc. Throughout applications indiverse fields (like above), extreme risks play an importantscientific, societal as well as (possibly) political role. Thedissemination of new statistical tools leading to a betterunderstanding of the occurrence of joint extremes is of greatimportance. This can be very well achieved at the level of newgraduate courses, publications in journals aimed at a broadenaudience and in discussion with scientists from other fields.