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

发布时间：2018-05-07 00:32

本文选题：交互信息 + 多元GARCH模型　；参考：《中国管理科学》2010年06期

【摘要】：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。
[Abstract]:In this paper, the generalized orthogonal GARCH model of Van der Weidei 2002 is extended, and a generalized orthogonal GARCH model with "leverage effect" is proposed, which reflects the volatility of financial asset returns. Because the extended generalized orthogonal GARCH model is difficult to estimate parameters in high-dimensional data, this paper studies the parameter estimation problem of the model from the perspective of interactive information theory. It is proved theoretically that the parameter estimation of multivariate GARCH model based on interactive information minimization is related to and different from that of parameter estimation based on maximum likelihood function. In the framework of the extended generalized orthogonal GARCH model, Different statistical techniques are used to realize the parameter estimation method based on the minimization of interactive information, which avoids the difficulty of correctly specifying the standardized residual probability density function and the high dimension operation in advance for the traditional maximum likelihood function estimation, and the calculation efficiency is high. The multivariate GARCH model can be applied to high dimensional data. Finally, based on the 15 stock index data of major global financial markets, the validity of the extended generalized orthogonal GARCH model and its parameter estimation methods are evaluated and tested by empirical research. The empirical study shows the advantages of the extended generalized orthogonal GARCH model and the parameter estimation method proposed in this paper.
【作者单位】：中央财经大学;南京大学;
【基金】：国家自然科学基金资助项目(70603034,70971145) 教育部人文社科项目(08JC790107) 中央财经大学“211工程”三期资助项目
【分类号】：F224;F830.9

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