风险度量半参数变系数复合Expectile回归模型及应用

The semiparametric varying-coefficient composite expectile regression model in risk measurement and its application

本文结合半参数变系数回归模型、期望分位数风险价值(EVaR)的思想以及充分利用多个Expectile信息能提高参数估计效率的假设,提出了一类半参数变系数复合Expectile回归模型,并对该模型进行了估计,建立了所提出复合Expectile回归(CER)估计的大样本性质.针对该模型既含有参数部分也含有非参数部分的特征,采用了方便计算的三步估计方法.通过数值模拟也发现,当误差为厚尾或非对称分布时,在均方根误差(RMSE)的标准下,所提出的CER估计大大优于最小二乘(LS)估计和简单的Expectile回归(ER)估计.另外,本文还应用所发展的理论分析了我国货币政策对上证综指的影响.

We propose a class of semiparametric composite expectile models with varying-coefficients via combining a semiparametric regression model with varying-coefficients,the EVaR thought and the assumption that using all information from multiple expectiles can improve the efficient of estimators.In this paper,we introduce estimation called composite expectile regression(CER),and we establish large sample properties of the resulting CER estimator.Based on the fact that the model includes the parametric part and the nonparametric part,we adopt a three-step estimating procedure.Our simulation studies demonstrate that our CER estimator is competent to the existing estimators,e.g.the least squares(LS)estimator or other expectile regression(ER)estimators,in the sense of root mean squared-error when the error follows a heavy-tailed or asymmetric distribution.In addition,we use the proposed method to analyze the relationship between China’s monetary policy and Shanghai Composite Index.