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 数学进展
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 股票收益率和新息的尾部估计(英文) Estimation of the Tails of Stock Returns and Innovations 柳会珍;顾岚; LIU Huizhen GU Lan 北京化工大学数学系,中国人民大学统计学系 北京,100029,北京,100872 (Department of Mathematics, Beijing University of Chemical Technology, Beijing, 100029, P. R. China; Department of Statistics, Renmin University of China, Beijing, 100872, P. R. China 收稿日期: 2008-02-25 出版日期: 2008-02-25
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 摘要 利用极值理论来考虑上证综指收益率的尾部.为了选择合理的超越门限,采用平均剩余函数和De-Haan矩估计相结合的方法.在学生t分布和广义误差分布的新息假设下,用GARCH和EGARCH新息的ARMA模型拟合指数收益率,并且使用极值理论的极大似然方法估计模型残差的尾指,估计结果表明收益率的尾指和模型的残差尾指基本一致. 关键词 ： 极值理论,  超越门限,  矩估计,  尾指,  GARCH Abstract：Extreme value theory is employed to consider the tails of Shanghai Index returns. To choose the reasonable exceedance threshold, mean excess function and De-Haan moment estimate are used. ARMA models with GARCH and EGARCH innovations following student-t distribution and generalized error distributions are fitted to the Index returns, and the tails indices for the models residuals are estimated by using maximum likelihood methods based on the extreme value theory. The results shows that the tail index of Index returns coincides largely with the ones of models residuals. Key words： exceedance threshold    moment estimate    tail index    GARCH
 [1] 王辉. 一元GARCH模型估计的渐近理论：平稳与非平稳情形[J]. 数学进展, 2013, 42(2): 138-152.
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