金融市场高维波动率的扩展广义正交GARCH模型与参数估计方法研究

An Extended Generalized Orthogonal GARCH Models for Multivariate Volatility in High Dimensional System of Finance Market and Its Parameter Estimation

本文对Van der Weide(2002)的广义正交GARCH模型进行扩展,提出反映金融资产收益波动性特征,具有"杠杆效应"的广义正交GARCH模型。由于这种扩展的广义正交GARCH模型在高维数据中面临参数估计困难,本文从交互信息理论视角研究模型的参数估计问题,在理论上证明基于交互信息最小化的多元GARCH模型参数估计与基于极大似然函数参数估计的联系和区别,并在提出的扩展广义正交GARCH模型框架下,采用不同的统计技术实现基于交互信息最小化的参数估计方法,避免了传统极大似然函数估计需要事先正确指定标准化残差概率密度函数和高维运算困难,计算效率较高,使多元GARCH模型在高维数据中可以应用。最后,根据全球主要金融市场的15种股票指数数据,通过实证研究对建立的扩展广义正交GARCH模型及其参数估计方法有效性进行评价与检验。实证研究表明了本文提出的扩展广义正交GARCH模型与参数估计方法的优势。

In this paper,an extended generalized orthogonal GARCH Model,which can reflect the asymmetry and leverage of volatility,is proposed based on that of Van der Weide（2002）.Then,a new estimation method for the multivariate GARCH models from the mutual information-theoretic viewpoint is considered.The relationship between the statistical dependence in standardized residuals and the maximum likelihood,when estimating multivariate GARCH models,is revealed.Based on that,the different statistic ways are proposed in the framework of the extended generalized orthogonal GARCH models,for purpose of implementing the models based on the estimation of mutual information minimization.These methodologies can therefore be easily applied to high-dimensional systems,where likelihood-based estimation will run into computational problems.According to 15 global stock returns indexes,empirical research is included to illustrate the model and the estimation method.