多元旋转自回归条件异方差模型的构建与应用研究——以九种人民币汇率波动为例

Research on the Construction and Application of Multivariate RARCH Models——Take Nine RMB Exchange Rates for Example

本文描述了新扩展的多元旋转自回归条件异方差(RARCH)模型与旋转条件相关(RCC)模型及其三种主要类型:Scalar、Diagonal和CP,说明了如何利用极大对数似然法进行参数估计,然后,以9种主要的人民币外汇汇率收益率序列为例,对这两个多元旋转自回归条件异方差模型进行了参数估计,并与OGARCH和GOGARCH模型进行了有效性比较。研究结果表明,在二元波动模型中,RARCH与RCC模型的拟合效果显著优于OGARCH与GOGARCH模型,而且,RCC模型受益于分步估计,可以首先得到各序列的边缘分布,再对动态波动的参数进行估计,因而其表现要好于RARCH模型;在多元波动模型中,CP类的RARCH与RCC模型的拟合效果稍劣于Diagonal类型,但所需估计的参数大幅度减少,这对于估计高维数据的动态波动非常有效。通过边缘Copula预测能力分解可以看出,RARCH和RCC与OGARCH及GOGARCH模型相比,在1步提前预测的联合似然值上,获得了统计显著的收益。

This paper presents a new extension of the multivariate ARCH model： RARCH model, which includes three forms： scalar, diagonal and common persistence. We show how to take advantage of the maximum logarithmic likelihood method to estimate parameters and make compare with RCC, OGARCH and GOGARCH model. Then we empirical study the return series of nine major foreign exchange rates in RMB. The research results show that RARCH and RCC models fit significantly to better than OGARCH and GOGARCH models in the binary model. RCC benefits from the step-by-step estimation which can first obtain the marginal distribution of each sequence, resulting in better performance than RARCH model. In multivariate volatility models, the RARCH-CP and RCC fit slightly inferior to the diagonal type. But it substantial reduces in the number of the estimated parameters, which is very effective in estimating the dynamic fluctuations of high-dimensional data.