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

SGER：极值统计及其在金融时间序列中的应用

• 批准号: 0443048
• 负责人: Zhengjun Zhang
• 金额: $ 3.86万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-15 至 2005-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0443048&HistoricalAwards=false
• 关键词: SGER; Statistics; Extremes; Applications; Financial

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.

本文提出了一系列关于尾部独立性的新检验方法和尾部相关性的新度量方法，特别是研究了极端相关系数、尾部相关性度量、Gamma检验统计量。这些都涉及到多元极值统计的研究。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协同运动指定新模型，并开发对这些协同运动更敏感的新投资组合评估工具。本文介绍了一种新的极端同动测度，包括发展最大稳定过程的统计估计方法。本文还介绍了如何利用组合马尔可夫过程和最大稳定过程模型来计算投资组合风险度量的方法，由于极值相关的所有定义都依赖于一些极限过程，并且通常涉及到参数在特定参数空间边缘的统计检验，因此必须非常小心地获得具有足够功效的检验。这项建议正是为了找到解决办法。研究人员将仔细比较和对比新的方法与现有的使用模拟以及真实的数据。真实的数据将来自保险、金融、电信、气候学、地震学、医学等不同领域。在不同领域的应用中（如上所述），极端风险扮演着重要的科学、社会以及（可能）政治角色。传播新的统计工具，使人们更好地了解联合极端事件的发生，这一点至关重要。这可以很好地实现在新的研究生课程的水平，在期刊上的出版物，旨在更广泛的受众，并在讨论与科学家从其他领域。