Estimation Of Dynamic Covariance Matrix Under Bernstein Condition

The covariance matrix plays a very important role in various fields of statistics,especially in high-dimensional data,that is,when the dimension is large relative to the sample size,it is challenging to estimate the high-dimensional covariance matrix.When estimating the high-dimensional covariance matrix,the more common processing methods are based on thresholding or shrinkage methods.However,in many applications(for example:regression,forecasting portfolio,portfolio selection),what we need is not the covariance matrix,but the inverse(accuracy matrix)of the covariance matrix.At present,many articles estimate the covariance matrix based on under static conditions,but it is not suitable for many practical applications.Recently,some scholars Chen and Leng(2016)proposed to use the threshold estimation method on the basis of sparse matrix to obtain the consistent convergence speed of high-dimensional dynamic covariance matrix.This paper will solve the estimation problem of high-dimensional dynamic covariance matrix based on a sparse matrix and Bernstein conditions.Under the high-dimensional dynamic covariance matrix estimation method proposed by Chen and Leng(2016),the exponential tail condition is changed.A method for estimating a high-dimensional dynamic covariance matrix is introduced under Bernstein conditions,and a consistent convergence rate is obtained through large sample theory,which is improved compared with the convergence rate proposed by Chen and Leng(2016).