Abstract: Value at Risk (VaR) is one of the most popular methods of measuring financial asset risk in the current finance industry. Calculating unconditional risk measure values based on autoregressive models (AR) is widely used in industries. Further investigation of this problem is valuable both in theory and application. In this paper, an estimating approach for autoregressive models based on weighted composite quantile regression (WCQR) is proposed. This new approach can make full use of information from several quantiles to improve the efficiency of parameter estimators, and given different weights for different quantiles regression, which result in making the estimation more efficient. The proposed estimator is shown to have asymptotic normality. Finite sample studies illustrate that when the error follows a non-normal distribution, the statistical properties of WCQR estimators are similar to those of maximum likelihood estimators. It implies that the proposed estimator is strongly competent to the existing estimators because the error is free of a specific distribution. The proposed method has a good application in the calculation of dynamic VaR. The empirical results via analyzing nine Chinese closed funds show that the VaR values based on WCQR method is similar to those based on the non-parametric method. In addition, one pronounced advantage based on the proposed WCQR estimation is that it can be used to calculate and forecast the values of dynamic VaR for asset returns.

Key words: autoregressive model, quantile regression, asymptotic normality, weighted composite quantile regression(WCQR) estimation, dynamic VaR