相依样本下半参数变系数期望分位数风险度量模型统计推断  

Semiparametric varying-coefficient expectile model for estimating value at risk on dependent samples

作　　者：王子剑 周勇[2] 曾凡平 Zijian Wang;Yong Zhou;Fanping Zeng

机构地区：[1]上海财经大学统计与管理学院,上海200433 [2]统计与数据科学前沿理论及应用教育部重点实验室,华东师范大学经管学部统计交叉科学研究院,上海200062 [3]广西财经学院信息与统计学院,南宁530003

出　　处：《中国科学：数学》2021年第9期1377-1406,共30页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:71331006,71931004和91546202)资助项目。

摘　　要：本文在α-混合序列假设下,基于半参数变系数模型研究条件期望分位数风险价值(expectile-based value at risk,EVaR)的风险度量.此模型不仅考虑了风险因素的影响,还可以动态描述风险影响及交互效应.同时,EVaR比经典的风险在险价值(quantile-based value at risk,QVaR)具有更直观、更易于计算的良好性质,而且对于资产分布的尾部损失更加敏感,在度量极端风险情形下,相对于QVaR更为有效和方便.本文采用三阶段估计的方法,分别对变系数部分和常系数部分的参数进行估计,并且给出3个阶段中每个估计的相合性和渐近正态性.为了节省计算时间,提高计算效率,本文采用一步估计的算法,减少迭代所需的时间.由于时间序列样本是非独立样本,建立这些统计量的大样本性质时带来了更大的困难.有别于独立同分布的观察数据,本文利用大小块分割方法发展α-混合序列的极限理论,获得了基于金融时间序列数据建立的模型参数和非参数估计的统计渐近性质.在数值模拟中,本文给出3个模型假设下变系数曲线估计和常系数估计的结果,无论是估计的精确度还是估计的稳健性,模拟结果都表明本文所提出的估计方法有优良的性质.实例则展示了本文所提出模型在上证指数的实际应用.We introduce a semiparametric varying-coefficient model to study the expectile-based value at risk(EVa R)based on theα-mixing assumption.The model considers the risk factors as well as the dynamic structure and the interaction of these factors.Meanwhile,EVa R not only has great advantages such as the subadditivity or easy to calculate,but also is very sensitive to the scale of losses compared with the conventional quantile-based value at risk(QVa R),which makes it as a more mature and efficient way of the risk measure in extreme risk situations.We develop a three-stage method to estimate the parameters of the varying-coefficient part and the constant-coefficient part.We also establish the challenging consistency and the asymptotic normality of all the resultant estimation in three stages under the time series samples.To save computing time,we propose to use a one-step procedure to compute the estimation.Financial time series samples are not independent data.It has more challenge to establish the large sample properties of the estimators.We introduce the dividing methods to prove the limit theory of theα-mixing series,and obtain the asymptotic properties of the parametric constant coefficients and the nonparametric varying-coefficients.In our simulation,three models’results show the accuracy and robustness of our estimation.The real financial data example performs as an application of our model at the end of our study.

关 键 词：Α-混合 半参数 变系数 期望分位数 在险价值 三阶段估计 

分 类 号：O211.67[理学—概率论与数理统计] F224[理学—数学]