| With the rapid development of information technology,high-dimensional data has widely appeared in fields such as biology,finance,and macroeconomics.The structure of these data is complex and not easy to analyze,but there is often a certain correlation between variables.How to simplify the data structure with the help of this correlation has become a important research direction in recent years.The high-dimensional factor model can transform the observed variables into a few latent variables,which can reflect most of the information of the observed variables,effectively simplify the data structure,and become an important tool for analyzing data.Determining the number of factors is important for estimation and prediction using highdimensional factor models.This paper establishes the factor number determination criterion by solving an equation about the eigenvalue of the sample correlation matrix,takes the root of the equation as the threshold for the number of selection factors,and demonstrates the effectiveness of the threshold through simulation.The simulation results show that the threshold given in this paper has good factor selection ability under specific circumstances,which is better than some existing factor number selection methods.In addition,the proposed factor number determination criterion is applied to the empirical analysis of the S & P 500 index dataset. |
