自回归模型的加权复合Expectile回归估计及其应用

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.

Weighted composite expectile regression estimate of autoregressive models with application

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.