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 heavytailed 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.