高维稀疏对角GARCH模型的估计及应用

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.

The Estimation and Application of High-dimensional Sparse Diagonal GARCH Model

Under the background of high dimensional data,it is no longer applicable because of the influence of data dimension and noise.Aiming at the deficiency of goGARCH model,we apply the high-dimensional sparse modeling to the estimation of goGARCH model,and propose a High-dimensional sparse diagonal GARCH (HDS-goGARCH) model.The regression coefficients of some unimportant variables are reduced to zero by introducing the penalty function,and the model is simplified to achieve the goal of reducing dimension.Through simulation and empirical studies,it is found that goGARCH model significantly improves the efficiency of estimation and prediction of large matrix,and the investment portfolio constructed by the HDS-goGARCH model is less risky in the case of certain income.