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-at-Risk的样本外预测也更加准确。
Dynamic higher moments is a stylized feature of financial returns. Empirical performance of the popular Generalized-t distribution (GT) and the Gram-Charlier series expansion of the Gaussian density (GCE) under GJRGARCH framework are compared in this paper, in terms of their capacity to fit time-varying higher moments and forecast Value-at-Risk. Using the daily returns of S&P 500 stock index in the U.S. and CSI300 stock index in China, it's shown that both return series exhibit time variation and persistence in conditional higher moments, and the persistence parameters of skewness are as high as 0.9. According to various statistical standards, both GT and GCE distribution have good empirical performance. GT models slightly outperform GCE models in fitting return distribution and forecasting extreme Value-at-Risk out-of-sample, despite some modeling advantages of GCE.
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