Abstract: GARCH model is a common tool to describe the return of assets, which is widely used in the field of risk measurement. In order to more effectively describe the characteristics of skewness and fat-tailedness of the return, more and more scholars have studied the condition distribution of the GARCH model. However, it is not enough to modify the conditional distribution of GARCH model only, and the function form of the model itself needs to be modified. Time-varying parameter modeling based on the score function thought has attracted much attention for recent years. This article uses this idea to model thetime-varying logarithmic standard deviation in the EGARCH model, and uses the EGB2 distribution as the conditional distribution of the model, and then sets up the GAS-EGARCH-EGB2 model. In this paper, the risk prediction effect of the GAS-EGARCH-EGB2 model is studied by the 10 Chinese industry indexes. The empirical results are as follows. Firstly, the daily logarithmic return series of 10 Chinese industry indices showthe characteristics of skewness, fat-tailedness and time-varying volatility. Secondly, in terms of return series fit, EGB2 distribution has excellent distribution fitting effect, both types of EGARCH models can significantly reduce the autocorrelation of the first four moments of the return series, and among them the EGARCH model based on the moment function is better. Thirdly, with respect to the in-sample and out-of-sample VaR prediction, EGB2 distribution is the best, but, two kinds of skewed Logistic distributions and two types of skewed hyperbolic secant distributions also have good VaR prediction effects, and asymmetric distribution is significantly better than symmetric distribution. In total, both types of EGARCH models have good VaR prediction effects, and among them the EGARCH model based on the score function is better.

Key words: EGB2 distribution, score function, moment function, EGARCH model, VaR forecasting

摘要： GARCH族模型是刻画资产收益率的常用工具,在风险度量领域具有广泛应用。为了更有效地描述收益率的偏斜厚尾等特征,越来越多学者对GARCH族模型的条件分布形式进行了研究。但是仅对GARCH模型条件分布进行修正是不够的,还需要对模型本身的函数形式进行修正。基于得分函数的时变参数建模思想近年来受到广泛关注,本文借助这一思想对EGARCH模型中对数标准差进行时变波动建模,并利用EGB2分布族作为模型的条件分布,进而建立GAS-EGARCH-EGB2模型。以我国10只中证行业指数为研究对象考察GAS-EGARCH-EGB2模型的风险预测效果,GAS-EGARCH-EGB2模型样本外VaR预测表现普遍优于ACM-EGARCH-EGB2模型。

关键词: EGB2分布, 得分函数, 矩函数, EGARCH模型, VaR预测