Abstract This paper discusses four GARCH-type models (A-GARCH, NA-GARCH, GJR-GARCH, and E-GARCH) in representing volatility of financial returns with leverage effect. In these models, errors are assumed to follow a Laplace distribution in order to deal with the typical leptokurtic feature of financial returns. The properties of these models are analyzed theoretically in terms of unconditional variance, kurtosis, autocorrelation function and news impact, and are further examined in the applications to real financial time series. Comparison is made with other choices of error distributions such as normal, Student-5, and Student-7 distributions, respectively. We also conduct residual analyses to justify the choice of error distributions and find that Laplace-E-GARCH model still performs very well. Our main purpose is to study and compare the proposed models’ relative adequacies and underlying limitations.

中文翻译：

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拉普拉斯误差下具有杠杆效应的波动率建模

摘要本文讨论了四种GARCH型模型（A-GARCH，NA-GARCH，GJR-GARCH和E-GARCH），它们用杠杆效应来表示财务收益的波动性。在这些模型中，假定误差遵循拉普拉斯分布，以处理典型的财务收益的瘦腿特征。从无条件方差，峰度，自相关函数和新闻影响等方面对这些模型的属性进行了理论分析，并在应用于实际财务时间序列中进行了进一步研究。将分别与其他错误分布选择进行比较，例如正态分布，Student-5和Student-7分布。我们还进行了残差分析以证明选择误差分布的合理性，并发现Laplace-E-GARCH模型的性能仍然很好。