| In the fields of economy,finance,biology,medicine and other sciences,researchers often encounter large and high-dimensional data.Factor models are favored by theoretical researchers and empirical researchers because they can effectively extract information from that.In recent years,the problem of factor number selection under large and high-dimensional data is a hot and difficult issue in the field of statistics and econometrics.Basically,the relevant literature published in top magazines introduces,optimizes or innovates the selection method of factor number every year.In this paper,Monte Carlo simulation experiments are carried out to compare the seven new and mainstream methods for determining the number of common factors in the approximation factor model.Based on the previous methods,this paper proposes two new methods for selecting the number of common factors.One is to determine the number of common factors in the approximate factor model by modifying the GR and TCR methods to combine the advantages of the two estimation methods,and name it the mixture ratio,referred to as MR.The other is to an extended eigenvalue difference test method by improving the compression function in the ED method proposed by Wu(2018)to determine the number of common factors in the approximate factor model,referred to as EED.It can be further shown that,comparing with the competitors,new methods has desired performance on truly selecting the value of the number of latent common factors,especially,the method MR has a better estimation effect in the presence of weak factors and the method EED has better estimation performance than other methods in the presence of the dominant factor.Finally,take the S&P 500 stocks which have 341 return series of 1916 days for example to construct the balance panel data,and then we estimate the factor numbers of S&P 500 stocks yield with above methods.It is concluded that the number of common factors is 2 based on the empirical data in the approximate factor models. |
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