二元极值混合模型相关结构的研究
Simulated Analysis of Bivariate Extreme Mixed Model
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摘要: 二元极值混合模型由于不能反映极值变量之间的完全相关性,因而在应用上受到了一定的限制,但对适当的相关性仍是一个很好的模型.本文给出了二元极值混合模型的一些基本性质,特别用随机模拟方法研究了对来自其它不同极值copula的随机样本,用混合模型拟合可能产生的影响. 结果表明,如果以Kendallτ表示变量间的相关性,在一定范围内,混合模型能够很好的反映其它模型所具有的相关性,且对渐近独立模型边际参数估计的偏差也不太大.最后应用混合条件分布与GEV条件分布分析英镑对美元和英镑对加元两支汇率日对数回报收益率的风险相关性.Abstract: Bivariate extreme mixed model can not reach the complete dependence of extreme variables, so it has a restriction in application. However, bivariate extreme mixed model still a good model for some dependence. In this paper we firstly introduce some basic knowledge about bivariate extreme mixed model. Specifically, we aim to assess the effects through a simulation study when a BEV distribution with mixed model dependence is fitted to data from other bivariate extreme value copula. As a result, if we measure dependence by Kendall’s τ, we find that to some extent mixed model can capture the dependence of other models. And for asymptotically independent model, the bias in the marginal parameters is not severe. At last, we use mixed conditional model and GEV conditional model to analysize the data about the log-daily returns of two exchange rates: UK sterling against both the US dollar and the Canadian dollar.