英文标题：
《Empirical Study of the GARCH model with Rational Errors》
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作者：
Ting Ting Chen and Tetsuya Takaishi
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最新提交年份：
2013
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英文摘要：
We use the GARCH model with a fat-tailed error distribution described by a rational function and apply it for the stock price data on the Tokyo Stock Exchange. To determine the model parameters we perform the Bayesian inference to the model. The Bayesian inference is implemented by the Metropolis-Hastings algorithm with an adaptive multi-dimensional Student\'s t-proposal density. In order to compare the model with the GARCH model with the standard normal errors we calculate information criterions: AIC and DIC, and find that both criterions favor the GARCH model with a rational error distribution. We also calculate the accuracy of the volatility by using the realized volatility and find that a good accuracy is obtained for the GARCH model with a rational error distribution. Thus we conclude that the GARCH model with a rational error distribution is superior to the GARCH model with the normal errors and it can be used as an alternative GARCH model to those with other fat-tailed distributions.
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中文摘要：
我们使用GARCH模型，该模型具有由有理函数描述的厚尾误差分布，并将其应用于东京证券交易所的股价数据。为了确定模型参数，我们对模型进行贝叶斯推理。贝叶斯推理由Metropolis-Hastings算法实现，该算法具有自适应的多维学生t-建议密度。为了将该模型与具有标准正态误差的GARCH模型进行比较，我们计算了信息标准AIC和DIC，发现这两个标准都支持误差分布合理的GARCH模型。我们还利用已实现的波动率计算了波动率的准确性，发现对于误差分布合理的GARCH模型，获得了很好的准确性。因此，我们得出结论，具有合理误差分布的GARCH模型优于具有正态误差的GARCH模型，并且可以作为具有其他厚尾分布的GARCH模型的替代模型。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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