Estimation Of The Number Of Common Factors In A Near-factor Model Based On ED Method As Parameter Selection

Over the past several decades,new technologies have changed the way data are collected,and now high-dimensional data is becoming more and more common.Factor model has been paid more and more attention because it can effectively extract infor-mation from high-dimensional data.In factor analysis,many decisions must be made,one of which is to choose the number of common factors.In this paper,we study the selection of the adjustment parameters in the ED esti-mation method for the number of common factors of approximate factor model.The approximate factor model studied in this paper is more extensive than the general fac-tor model.First of all,the data type is aimed at panel data.Panel data can overcome the problem of multiple collinearity in time series analysis,and has many advantages.Compared with the classical factor model,the approximate factor model allows for se-quence correlation and cross section dependence of heterogeneous components in the model,which is more in line with the more and more complex data structure.So far,many statisticians have proposed methods to estimate the number of factors in the approximate factor model.Wu（2018）^[1]proposed an eigenvalue difference type estimate for the approximate factor model with dominant factors.The transformation function is used to compress the eigenvalues in order to weaken the influence of the dominant factor.Due to its methodology novelty and large effects on the large eigen-values resulted from dominant factors,the method of Wu（2018）^[1]deserves attention and further research.In this paper,based on method proposed by Wu（2018）^[1]for es-timating the number of common factors in the near factor model,in order to solve the remaining regulation parameter selection problem in the conversion function,the paper uses the idea of parameter optimization proposed by Hallin and Liaka（2007）^[2]in the dynamic factor model.We introduce a method to select the adjustment parameter based on the selection of subsamples for stability test.Monte Carlo simulation results in chap-ter four show that compared with many previous methods of factor number estimation,the results have great advantages,especially in the presence of principal factors.