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自回归模型的加权复合Expectile回归估计及其应用
引用本文:刘晓倩,周勇.自回归模型的加权复合Expectile回归估计及其应用[J].系统工程理论与实践,2016,36(5):1089-1098.
作者姓名:刘晓倩  周勇
作者单位:1. 上海外国语大学 国际金融贸易学院, 上海 200083;2. 上海财经大学 统计与管理学院, 上海 200433;3. 中国科学院 数学与系统科学研究院, 北京 100190
基金项目:国家自然科学基金(71271128);2015年度教育部人文社会科学青年基金项目(15YJC910004);上海外国语大学青年基金项目(2015114051)
摘    要:本文基于充分利用多个Expectile信息能提高参数估计效率的假设,提出了AR模型的加权复合Expectile回归(WCER)估计,探讨了该估计的最优权重,建立了其大样本性质,发现根据由数据驱动的最优权重所获得的WCER估计与最优权重已知时所获得的WCER估计具有相同的渐近有效性.数值模拟表明,当误差为厚尾或非对称分布,所提出的WCER估计大大优于传统最小二乘估计.即使误差分布未知,依然可以得到像极大似然估计一样具有优良统计性质的WCER估计.应用所提出的方法分析恒生指数和标准普尔500指数,实证分析表明:所提出的WCER估计在有效性意义下非常具有竞争力.

关 键 词:自回归(AR)模型  Expectile回归(ER)  加权复合Expectile回归(WCER)  渐近正态  
收稿时间:2014-10-18

Weighted composite expectile regression estimate of autoregressive models with application
LIU Xiaoqian,ZHOU Yong.Weighted composite expectile regression estimate of autoregressive models with application[J].Systems Engineering —Theory & Practice,2016,36(5):1089-1098.
Authors:LIU Xiaoqian  ZHOU Yong
Institution:1. School of Economics and Finance, Shanghai International Studies University, Shanghai 200083, China;2. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China;3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Abstract:Based on the assumption that using all the information from multiple expectiles can improve the efficient of estimators, we propose a weighted composite expectile regression (WCER) estimation for AR models, investigate optimal weights of the resulting WCER estimator and establish its large sample properties. We also discover that the WCER estimators whose weight is data-driven and whose weight are known has the same asymptotic efficient. Simulation studies tell us that our WCER estimator greatly outperforms the least squares estimator in the sense of mean squared-error when the error follows a heavy-tailed or asymmetric distribution. Even if the distribution of the error is unknown, we can obtain a WCER estimator with nice statistical properties just like ones of a maximum likelihood estimator. The empirical analyses on the Hang Seng Index and the standard & Poor's 500 index demonstrate that the proposed WCER is competent in the sense of efficiency.
Keywords:autoregressive (AR) model  expectile regression (ER)  weighted composite expectile regression (WCER)  asymptotic normality
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