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动态时变高阶矩是金融收益率的一个重要特征。本文对比研究了主流的Generalized-t分布(GT)和Gram Charlier Expansion分布(GCE)在GJRGARCH模型下对动态高阶矩的拟合能力和Value-at-Risk的预测能力。基于2005—2014美国标普500股指和中国沪深300股指日收益率的实证结果显示,收益率的条件高阶矩存在显著的时变性和持续性,其中偏度参数的持续性参数达到0.9以上。从各种统计指标综合来看,这两种方法都具有较好的实证表现。尽管GCE分布具有某些高阶矩建模的便利性,GT分布的实证拟合能力更强,对极端概率Value-atRisk的样本外预测也更加准确。
Dynamic time-varying higher moments are an important feature of the financial rate of return. In this paper, we compare the ability of the mainstream Generalized-t distribution (G-GR) and the Gram Charlier Expansion distribution (GCE) to fit the dynamic higher-order moments and predict the Value-at-Risk under the GJRGARCH model. Based on the empirical results of the daily returns of the S & P 500 Index and the CSI300 Index of China from 2005 to 2014, the high-order moments of the yield rate have significant time-varying and persistent effects, of which the persistent parameters of the skewness parameters reach 0.9 . From a comprehensive analysis of various statistical indicators, these two methods have good empirical performance. Although the GCE distribution has the convenience of some higher order moments modeling, the empirical fit of the GT distribution is more robust and the out-of-sample prediction of the extreme probability Value-atRisk is more accurate.