高维条件协方差矩阵的非线性压缩估计及其在构建最优投资组合中的应用  

Nonlinear Shrinkage Estimation of High Dimensional Conditional Covariance Matrix and its Application in Portfolio Selection

作　　者：赵钊[1] 

机构地区：[1]华中科技大学经济学院,湖北武汉430074

出　　处：《中国管理科学》2017年第8期46-57,共12页Chinese Journal of Management Science

基　　金：国家自然科学基金面上资助项目(71671070)

摘　　要：本文将非线性压缩方法运用到DCC和BEKK模型中,用非线性的压缩估计量代替MMLE估计中初始的样本协方差矩阵,大大提高了高维DCC和BEKK模型的估计效率,并突破性地使得横截面维度大于时间维度时,DCC和BEKK模型的有效估计成为可能。蒙特卡洛模拟发现:非线性压缩方法对于DCC和BEKK模型估计的优化作用显著,且优化程度随着横截面维度和时间维度的比值增大而增加。实证分析进一步说明了非线性压缩方法对于准确估计高维条件协方差矩阵、从而提高组合选择效率的重要作用。It is well known that the traditional maximum likelihood estimation of GARCH model is severely biased in high dimensions.In this paper,the nonlinear shrinkage method proposed by Ledoit and Wolf is used to estimate DCC and BEKK models.In particular,the initial sample covariance estimator in maximum m-profile quasi-likelihood estimation(MMLE)proposed by Engle et al.is substituted by the nonlinear shrinkage estimator,which turns out to largely improve the estimation efficiency of high dimensional DCC and BEKK models,and for the first time,makes the valid estimation possible when the sample size is larger than the time series dimension.Based on the Percentage Relative Improvement in Average Loss(PRIAL),the Monte-Carlo simulations verify the obvious superiority of the nonlinear shrinkage substitution over the usual DCC and BEKK,which even strengthens as the ratio between sample size and time series dimension increases.Besides,for both DCC and BEKK,the performance of nonlinear shrinkage estimation is better than that of linear shrinkage,while linear shrinkage estimation is better than the usual estimation.Furthermore,the performance of DCC is better than BEKK,and the optimizing effect of nonlinear shrinkage on DCC is more significant than on BEKK.Finally,in the empirical part,using daily stock return data from the Center for Research in Security Prices(CRSP),the global minimum variance(GMV)portfolios of stocks traded in NYSE and NASDAQ are constructed based on various methods,and their real variances are compared.The empirical result supports the important role nonlinear shrinkage plays in promoting the estimation of high dimensional conditional covariance matrix,and thus in optimizing the portfolio selection.

关 键 词：非线性压缩 线性压缩 条件协方差矩阵 

分 类 号：F830.59[经济管理—金融学] O212.1[理学—概率论与数理统计]