針對均值-方差最佳化的巨大共變異反矩陣估計

Abstract

近幾年來透過因子分析(factor analysis)來估計高維度下的共變異矩陣(high dimensional covariance matrix)是越來越受歡迎，但要應用因子分析來估計在高維度下的共變異矩陣的反矩陣(high dimensional precision matrix)是非常的困難，因為在估計高維度誤差的共變異矩陣的反矩陣(high dimensional error precision matrix)當中，通常都含有稀疏(sparse)的限制。這篇論文結合了 modified Cholesky decomposition 以及 orthogonal greedy algorithm (OGA)的方法來估計在稀疏限制下高維度誤差的共變異矩陣的反矩陣，並應用在財務上 mean-variance portfolio optimization 的問題。在模擬的結果中，我們所提的方法比傳統的 threshold 來的更好。

Recently, it has drawn attention on estimation of high-dimensional covariance matrices by using factor analysis. However, it is very difficult to apply factor analysis estimation of high-dimensional precision matrices. Because one of the commonly used conditions for estimating high-dimensional error precision matrix is to assume the covariance matrix to be sparse. This study combine modified Cholesky decomposition and orthogonal greedy algorithm (OGA) approaches to estimate the high-dimensional precision matrix under the constraint that the covariance matrix is sparse. The result can be used to deal with the mean-variance portfolio optimization problem. According to the simulation results, the proposed approach outperforms the adaptive thresholding method.