Estimation And Application Of High Dimensional Covariance Matrix Based On High Frequency Data

The continuous innovation of information technology makes the storage and use of highfrequency data more convenient.Compared with the low-frequency data,the high-frequency data contains more information,and shortens the time span of the required samples,and the covariance estimated based on the high-frequency data is more effective.At the same time,with the development of financial market,the types of configurable assets are increasing,and the dimension of modern portfolio object has been extended to high dimension.For such highfrequency and high-dimensional data,it is very difficult to estimate the covariance matrix.First of all,the use of high-frequency data has the influence of microstructure noise,and the asset return in the real market has the non normality of peak and heavy tail,which leads to it that the estimation effect of traditional covariance matrix estimation method is unsatisfactory.Secondly,when the total dimension exceeds the sample size,the traditional estimation method will face the curse of dimension.For the estimation of high-dimensional covariance matrix of high-frequency data,this paper proposes a shrinkage model based on Huber loss function pre average mechanism.Based on the realized volatility theory,the model realizes the estimation of the integration covariance matrix of the high-frequency data by the shrinkage method combined with the high-frequency data processing mechanism.The contraction estimation is an important estimation method which is extended to the field of high-frequency data.It also provides method support for accurate estimation of high-dimensional covariance matrix of high-frequency data.In order to test the effectiveness of the proposed method,this paper compares the effects of different estimators through numerical simulation.The results show that the geometric shrinkage estimator based on Huber loss function pre average mechanism is the best.In this paper,the research ideas of the estimation method are further applied to the Chinese stock market,and the obtained estimator is combined with the minimum variance portfolio model to construct different asset portfolio types.The results show that the portfolio constructed by geometric shrinkage estimator based on Huber function pre average mechanism brings higher returns,and its portfolio volatility(risk)is also the smallest,and the sharp ratio is also higher than other covariance matrix estimators,which shows that the realized covariance matrix estimated by geometric shrinkage method based on Huber function pre average mechanism is the investment portfolio can make investors get higher returns.