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高维数据背景下,数据维度和噪声的影响使得传统的GARCH模型不再适用.针对对角GARCH(goGARCH)模型的不足,将高维稀疏建模法应用到其估计过程中,提出了高维稀疏对角GARCH(HDS-goGARCH)模型.HDS-goGARCH模型通过引入惩罚函数,将一些不重要变量的回归系数压缩为零,来精简模型,达到降维的目的.通过模拟和实证研究发现:较传统的goGARCH模型而言,HDS-goGARCH模型明显提高了高维协方差阵的估计和预测效率;并且将其应用在投资组合时:在收益一定的情况下,由HDS-goGARCH模型所构造的投资组合的风险更小.
Due to the influence of data dimension and noise, the traditional GARCH model is no longer suitable for high-dimensional data.For the shortcomings of the diagonal GARCH (goGARCH) model, a high-dimensional sparse modeling method is applied to the estimation process, and a high dimensional The model of HDS-goGARCH is obtained.HDS-goGARCH model can reduce the dimensionality by introducing penalty function and compressing the regression coefficients of some unimportant variables to zero.Through the simulation and empirical research, In the case of the traditional goGARCH model, the HDS-goGARCH model significantly improves the estimation and prediction efficiency of the high-dimensional covariance matrix; and when it is applied to the portfolio, the portfolio constructed by the HDS-goGARCH model The risk is smaller.