Estimation Of Covariance Matrix In Large Dimensional Financial Data

The covariance matrix has been widely used in many aspects of financial analysis such as asset portfolio analysis.But the sample covariance estimation has limitations and the covariance of high-dimensional data is hard to be estimated,which leads to further study of covariance matrix estimation.In this paper we introduces the limitations of the sample covariance matrix.Based on the characteristics of financial data analysis,two methods are introduced to estimate the covariance matrix: thresholding estimation methods(including universal thresholding,adaptive thresholding and Principal Orthogonal Complement Thresholding)and shrinkage estimation methods.They are compared and analyzed.They both impose structural characteristics of financial data to sample covariance.But the thresholding method tries to sparse the elements of matrix,and the shrinkage estimation method tries to impose structure to the whole covariance.They both improve the estimation of sample covariance.In the analysis of financial time series data,observations at different times affect different.So this paper proposes an exponential smoothing sample covariance estimation.It can not only improve the sample covariance estimation,but also improve the thresholding estimation and shrinkage estimation.According to the real data of 100 stocks,it can be verified that in the analysis of financial time series data,the exponential smoothing sample covariance method makes the estimation better.At the same time,the improved thresholding method and shrinkage method by the exponential smoothing sample covariance are also make the estimations better than the original models.In the results,with the appropriate smoothing factor and window width,the improved thresholding method and shrinkage method by exponential smoothing sample covariances are improved by 6%to 12% compared with the original models.