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

We introduce a semiparametric varying-coefficient model to study the expectile-based value at risk (EVaR) based on the α-mixing assumption. The model considers the risk factors as well as the dynamic structure and the interaction of these factors. Meanwhile, EVaR 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 (QVaR), 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 the α-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.