Research On Parametric Estimation And Applications For Extreme Value Statistical Models

Extreme value events are rarer than those already recorded, but profoundin?uences are produced when they occur. The production and development ofextreme value theory provide theoretical bases for these random events. In thisdissertation, the properties and parametric estimations of extreme value modelsand their applications are studied intensively. As a result of these researches,several extreme value models based on extreme value theory are analyzed. TheBayes methodology to be used within extreme value analysis is also proposed.And dependence models based on extreme value theory and Copula function arealso investigated systematically. Some discussions are done for tail dependence ofextreme observations. The main achievements of this work are listed as follows:1. The key point of the mathematics statistics is inference. And the para-metric estimation is one of the main contents in inference. In this paper aframework—the Bayes methodology is proposed and the Markov Chain MonteCarlo techniques are used to make random observations which have posteriordistribution. Annual data recorded of highest water level in survey stations ofHuangpu River are analyzed. And some results are slightly high compared withthose of the corresponding likelihood method.2. Dependence analysis is a central issue in portfolio construction. Combinewith extreme value models and Copula functions together, M-Copula-GPD modelis established. Estimation and test methods of M-Copula-GPD are studied too.This model is used to study the degree and patterns of dependence betweenShanghai and Shenzhen stock markets. The empirical results show that non-symmetric pattern exists between the two markets.3. Extreme events which locate at the two sides of the distribution aresmall rate a?airs from the meaning of statistics. And extreme value theory focuson these types of events by luck. Two dependence measures and associatedwith the coe?cient of tail dependence are provided in this paper. Based onthese discussions, Novel diagnostic measures for dependence about returns andtransaction volumes of Shanghai stock index are studied. The conclusions drawnare as follows: weak extremal dependence for the stock data.4. As a valid financial risk tool, VaR has already been accepted extensively, and its calculation method also got a continuous improvement. Several methodsexisted currently to estimate VaR are analyzed and comprised. GARCH-GPDmodel are pointed and used to Shenzhen stock index. The empirical results showthat the GARCH-GPD model can thoroughly capture the volatility when fat-tailed densities are taken into account. And its conclusion is more secure thanother model's. Moreover, CVaR is discussed in this paper.