Inference in ARCH and GARCH models with heavy-tailed errors
Inference in ARCH and GARCH models with heavy-tailed errors
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DOI：
10.1111/1468-0262.00396
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发表时间：
2003-01-01
期刊：
影响因子：
6.1
通讯作者：
Yao, QW
中科院分区：
文献类型：
--
作者：
Hall, P;Yao, QW
ARCH和GARCH模型直接解决了条件二阶矩的依赖性，并且已被证明在存在相对较大波动的建模过程中特别有价值。这些包括金融时间序列，这可能是，特别重尾。然而，鲜为人知的是，在重尾设置的ESTA或GSTA模型的属性，没有方法可用于近似的参数估计的分布。在本文中，我们证明了，对于重尾误差，拟极大似然参数估计的渐近分布在ESTA和GSTA模型是非正态的，特别是难以估计直接使用标准的参数方法。标准的自助方法也不能产生一致的估计。为了克服这些问题，我们开发了一个子样本Bootstrap近似估计分布。采用学生化方法来近似尺度，采用子样本自助法来估计形状。这种方法的良好性能的理论和数值证明。
ARCH and GARCH models directly address the dependency of conditional second moments, and have proved particularly valuable in modelling processes where a relatively large degree of fluctuation is present. These include financial time series, which can be, particularly heavy tailed. However, little is known about properties of ARCH or GARCH models in the heavy-tailed setting, and no methods are available for approximating the distributions of parameter estimators there. In this paper we show that, for heavy-tailed errors, the asymptotic distributions of quasi-maximuni likelihood parameter estimators in ARCH and GARCH models are nonnormal, and are particularly difficult to estimate directly using standard parametric methods. Standard bootstrap methods also fail to produce consistent estimators. To overcome these problems we develop percentile-t, subsample bootstrap approximations to estimator distributions. Studentizing is employed to approximate scale, and the subsample bootstrap is used to estimate shape. The good performance of this approach is demonstrated both theoretically and numerically.