Dependence modeling via copulas: inference, theoretical study and applications

通过联结函数进行依赖建模：推理、理论研究和应用

• 批准号: 327108-2006
• 负责人: Quessy, JeanFrançois
• 金额: $ 1.02万
• 依托单位: Université du Québec à Trois-Rivières
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2008
• 资助国家: 加拿大
• 起止时间: 2008-01-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=397580
• 关键词: Dependence; modeling; via; copulas; inference

Copula theory provides powerful and flexible tools helping to model phenomena that imply many random variables. The proposed research project concerns the use of copulas in various contexts of application. It is divided in four parts: First, statistical methods that allow the selection of an appropriate family of copulas will be developed. The classical situation of independent and identically distributed observations, as well as the time series context, will be treated. The asymptotic validity of the proposed techniques will be demonstrated using the  theory of empirical processes. Special attention will be given to applications in the domain of statistical hydrology, where multivariate time-dependent observations are often collected. In the second part, tests for the independence between random variables and/or vectors will be proposed and evaluated from the point of view of their asymptotic efficiency. Appropriate versions of the empirical copula process will enable to generate interesting classes of tests of independence in these contexts. In the third part of the project, the dependence structures induce by multivariate conditional distributions will be investigated. The special cases of Archimedean and elliptical distributions will be studied in details. These laws exhibit the interesting property of remaining in the same class of models when a conditioning is applied. Finally, the fourth part of the project will be devoted to an important problem in finance and actuarial science, namely the risk evaluation of a portfolio of many assets. Bounds on the risk that balance for the lack of information on the nature of the dependence among the assets will be computed for various portfolios.

Copula理论提供了强大而灵活的工具，有助于对包含许多随机变量的现象进行建模。拟议的研究项目涉及在各种应用环境中使用copula。它分为四个部分：第一，统计方法，允许选择一个适当的家庭copula将开发。经典的独立和同分布的观测值的情况下，以及时间序列的背景下，将被处理。所提出的技术的渐近有效性将使用经验过程的理论来证明。将特别关注统计水文学领域的应用，其中经常收集多元时间相关观测值。在第二部分中，随机变量和/或向量之间的独立性的测试将提出和评估的角度来看，他们的渐近效率。适当的版本的经验copula过程将能够产生有趣的类的独立性测试在这些情况下。本计画的第三部分将探讨由多元条件分布所引起的相依结构。阿基米德分布和椭圆分布的特殊情况将被详细研究。这些法律表现出有趣的性质，保持在同一类模型时，条件是适用的。最后，该项目的第四部分将专门讨论金融和精算学中的一个重要问题，即对许多资产的组合进行风险评估。将为各种投资组合计算由于缺乏关于资产之间依赖性的性质的信息而平衡的风险的界限。