The extremogram and the cross-extremogram for a bivariate GARCH(1, 1) process
The extremogram and the cross-extremogram for a bivariate GARCH(1, 1) process
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双变量 GARCH(1, 1) 过程的极值图和交叉极值图
DOI：
10.1017/apr.2016.51
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发表时间：
2016
影响因子：
1.2
通讯作者：
Muneya Matsui and Thomas Mikosch
中科院分区：
文献类型：
--
作者：
陶山淑子;福岡晃平;森田真紀;八木俊路朗;久留一郎;Muneya Matsui and Thomas Mikosch
我们推导出二元 GARCH(1,1) 过程的极值图和交叉极值图的渐近理论。我们表明，双变量 GARCH(1,1) 过程的分量尾部可能表现出幂律行为，但根据参数的选择，分量的尾部索引可能会有所不同。我们将该理论应用于股票价格和外汇汇率的五分钟回报数据。我们通过考虑残差的样本极值图和交叉极值图来判断双变量 GARCH(1,1) 模型的拟合度。结果与二维创新序列的独立同分布假设一致。零滞后处的交叉极值图具有明显不同于零的值。这一事实表明创新的组成部分存在某种强烈的极端依赖性。
We derive asymptotic theory for the extremogram and cross-extremogram of a bivariate GARCH(1,1) process. We show that the tails of the components of a bivariate GARCH(1,1) process may exhibit power-law behavior but, depending on the choice of the parameters, the tail indices of the components may differ. We apply the theory to five-minute return data of stock prices and foreign-exchange rates. We judge the fit of a bivariate GARCH(1,1) model by considering the sample extremogram and cross-extremogram of the residuals. The results are in agreement with the independent and identically distributed hypothesis of the two-dimensional innovations sequence. The cross-extremograms at lag zero have a value significantly distinct from zero. This fact points at some strong extremal dependence of the components of the innovations.