Covariance Matrix Estimation And Its Application In Portfolios

With Markowitz's theory of mean-variance portfolio,which makes the theory of portfolio investment into the era of quantitative research,it also means the birth of modern securities portfolio theory.However,the mean-variance portfolio model requires the input of two parameters(mean vector and covariance matrix),but in practice the mean vector and covariance matrix are unknown.How to estimate the covariance matrix into the academic research topic.Although there are many methods in the existing literature that can estimate the covariance matrix,the estimation effect of these methods is not ideal and the process is complex and computationally large in the case of high dimensional yield data.Burns proposed that the PC-GARCH model can easily estimate the covariance matrix of the high-dimensional yield series.The main idea of the PC-GARCH model is a process of re-parametering.The PC-GARCH model uses the principal component analysis to map the original yield data into orthogonal principal component data.Assume that each principal component and each yield data follow the process of the univariate GARCH model,so that by estimating the correlation coefficient matrix and each the variance of the yield,so as to achieve the purpose of estimating the covariance matrix.PC-GARCH model to avoid the establishment of multiple GARCH model,only need to build a single variable GARCH model,greatly reducing the need to estimate the parameters,making the calculation of PC-GARCH model greatly reduced,but the covariance matrix estimation effect is not ideal.In order to reduce the computational cost,we can improve the accuracy of covariance matrix estimation.Therefore,this article has done the following work:(1)In this paper,we study the influence of the number of selected stocks in the mean-variance portfolio model on the optimal investment weight of the model.This paper mainly studies this problem from the perspective of simulation analysis.(2)Based on the PC-GARCH model,this paper proposes the MPC-GARCH model.The MPC-GARCH model is mainly to extend the process of PC-GARCH model assuming that each principal component and each yield data obey the univariate GARCH model.The MPC-GARCH model assumes that the principal component and the single yield data are obeyed Variable GARCH model,EGARCH model,GJR-GARCH model(also assume that the residuals of each model obey the normal distribution,t distribution,generalized error distribution,partial t distribution),and this paper uses the AIC criterion and BIC criteria to select the principal components And the best yield of each yield data,so as to improve the effect of the variance estimation of each principal component and each yield,and to improve the accuracy of covariance matrix estimation.(3)In this paper,a set of data was simulated by BEKK-GARCH(1,1)model,and the MPC-GARCH model,PC-GARCH model,DCC-GARCH model,CCC-GARCH model,BEKK-GARCH model and EWMA model were compared.Matrix prediction effect.(4)Based on the empirical analysis of the stock data of Lu and Shenzhen Stock Exchange,the MPC-GARCH model,PC-GARCH model,DCC-GARCH model,CCC-GARCH model,BEKK-GARCH model,EWMA model are used to analyze the covariance matrix Forecasting performance and portfolio performance constructed by its predicted covariance matrix.From the point of view of simulation analysis,the more the number of selected stocks in the mean-variance portfolio model,the better the investment effect of the optimal investment weight of the model.The results of simulation analysis and empirical analysis show that the MPC-GARCH model is better than the PC-GARCH model in the MPC-GARCH model.Compared with other models,the MPC-GARCH model has the same effect on the covariance matrix DCC-GARCH model,but the MPC-GARCH model takes much less time than the DCC-GARCH model and has a computational cost advantage.