Study On Kernel Density Estimation And Some Properties Of Copula

Dependence analysis of multidimensional random variables, which can be stud-ied effectively by the tool of Copula, is one of the main subjects in the study of statistics. In recent years, the Copula theory and Copula models are widely applied in many fields, such as financial risk management, investment portfolio, stock anal-ysis, and so on. In this dissertation, we mainly study the properties and the kernel density estimation of Copula. The main work can be concluded into several items.1. We review the development history of Copula theory, introduce the situation of the research and its applications in the financial field. Also. the significance of this study is mentioned.2. A new class of Copula is given. At the same time, some equivalent char-acterizations and properties are obtained. Moreover, some potential applications of one important property of Archimedes Copulas are presented. The two kinds of functions are compared and analyzed.3. After introducing the parameter estimation and nonparametric estimation of Copula, we focus on the kernel density estimation of bivariate Copulas. Using the strong approximation of quantile process and center limit theorem, we derive the convergence speed on the kernel density estimation of Copulas.4. As a numerical example, basing on kernel estimation method, we analyze the dependence of the data of the Shanghai Composite Index and Shenzhen composite index from 2014 to 2015.