加权复合分位数回归方法在动态VaR风险度量中的应用

Weighted Composite Quantile Regression Method of Dynamic VaR risk Measure and Their Applications

风险价值(VaR)因为简单直观,成为了当今国际上最主流的风险度量方法之一,而基于时间序列自回归(AR)模型来计算无条件风险度量值在实业界有广泛应用。本文基于分位数回归理论对AR模型提出了一个估计方法——加权复合分位数回归(WCQR)估计,该方法可以充分利用多个分位数信息提高参数估计的效率,并且对于不同的分位数回归赋予不同的权重,使得估计更加有效,文中给出了该估计的渐近正态性质。有限样本的数值模拟表明,当残差服从非正态分布时,WCQR估计的的统计性质接近于极大似然估计,而该估计是不需要知道残差分布的,因此,所提出的WCQR估计更加具有竞争力。此方法在预测资产收益的VaR动态风险时有较好的应用,我们将所提出的理论分析了我国九只封闭式基金,实证分析发现,结合WCQR方法求得的VaR风险与用非参数方法求得的VaR风险非常接近,而结合WCQR方法可以计算动态的VaR风险值和预测资产收益的VaR风险值。

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 ap- plication. 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 quan- tiles 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 distri- bution, the statistical properties of WCQR estimators are similar to those of maximum likelihood estima- tors. It implies that the proposed estimator is strongly competent to the existing estimators because the er- ror is free of a specific distribution. The proposed method has a good application in the calculation of dy- namic 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 ad- vantage based on the proposed WCQR estimation is that it can be used to calculate and forecast the values of dynamic VaR for asset returns.