基于改进MCD方法的多元GARCH模型的估计  

Estimation of Multivariate GARCH Model Based on Improved MCD Method

作　　者：刘丽萍[1] 徐宇欣 Liu Liping;Xu Yuxin(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025,China)

机构地区：[1]贵州财经大学数学与统计学院,贵阳550025

出　　处：《统计与决策》2020年第16期18-22,共5页Statistics & Decision

基　　金：国家社会科学基金资助项目(16CTJ013)。

摘　　要：多元GARCH模型常用于资产间协方差阵的估计和预测,但在高维数据背景下,维数诅咒、噪声影响使得传统的多元GARCH模型不再适用。文章考虑将改进的MCD方法应用到常见的多元GARCH模型——DCC和BEKK的估计过程中,提出基于改进MCD方法的多元GARCH模型,该模型在解决维数诅咒的同时,还考虑了资产的排列顺序对协方差阵估计的影响。通过模拟和实证研究发现:新提出的模型估计和预测的协方差阵更加接近于真实的协方差阵,其在投资组合中的应用效果更好,提高了投资者的平均收益,并降低了组合风险。The multivariate GARCH model is often used to estimate and predict the inter-asset covariance matrix. However,in the context of high-dimensional data, the curse of dimensionality and the influence of noise make the traditional multiple GARCH model no longer applicable. This paper considers applying the improved MCD method to the estimation of DCC and BEKK, the common multivariate GARCH models, and proposes the multivariate GARCH model based on improved MCD method.The model not only solves the curse of dimension, but also considers the influence of asset order on the estimation of covariance matrix. Simulation and empirical studies find that the estimation by the newly-proposed model and the predicted covariance matrix are closer to the real covariance matrix, and its application in the portfolio is more effective, which improves the average return of investors and reduces portfolio risk.

关 键 词：高维协方差阵 修正的乔列斯基分解法 惩罚函数 多元GARCH模型 

分 类 号：O21[理学—概率论与数理统计]