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近来,人们对实际数据使用厚尾分布进行建模颇感兴趣。一种流行的考虑就是所谓的广义自回归条件异方差(GARCH)模型。不幸的是,在一些应用中正态新息的GARCH模型的尾部不够厚。文章提出新息为正态方差混合分布的GARCH模型并给出了使用EM算法对模型参数作估计的步骤。结果表明,新息为正态方差混合新息分布的GARCH模型比正态新息的GARCH模型有更厚的尾部,因而更能捕捉实际数据中的厚尾特征。文章还以上证指数为例阐述了这一结论。
Recently, people are interested in modeling real-world data using thick-tailed distributions. A popular consideration is the so-called generalized autoregressive conditional heteroskedasticity (GARCH) model. Unfortunately, the tail of a normally attractive GARCH model is not thick enough in some applications. In this paper, we propose a GARCH model with a new distribution of variance as a normal variance and give the steps of using the EM algorithm to estimate the model parameters. The results show that the GARCH model with the new interest mixed variance distribution has a thicker tail than the normal new interest GARCH model, so it can better capture the thick tail features in the real data. The article also expounded this conclusion by taking the Shanghai Composite Index as an example.