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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。
This paper extends the generalized orthogonal GARCH model of Van der Weide (2002) and proposes a generalized orthogonal GARCH model that reflects the volatility of the return on financial assets and has a “leverage effect”. Since this extended generalized orthogonal GARCH model faces difficulties in parameter estimation in high-dimensional data, this paper studies the problem of parameter estimation from the perspective of interactive information theory, and theoretically proves that the estimation of multivariate GARCH model based on minimization of interaction information and the estimation based on Maximum likelihood function parameter estimation. In the framework of the proposed extended generalized orthogonal GARCH model, different statistical techniques are used to realize the parameter estimation based on minimization of mutual information, which avoids the traditional maximum likelihood function estimation It is necessary to correctly specify the normalized residual probability density function and the high dimensional operation difficulty in advance, and the calculation efficiency is high so that the multiple GARCH model can be applied in the high-dimensional data. Finally, according to the 15 stock index data of the world’s major financial markets, the validity of the extended generalized orthogonal GARCH model and its parameter estimation method is evaluated and verified through empirical research. Empirical studies show the advantages of extending the generalized orthogonal GARCH model and parameter estimation methods proposed in this paper.