The fluctuation of eigenvalues in factor models

We consider the fluctuation of eigenvalues in factor models and propose a new method for testing the model. Based on the characteristics of eigenvalues, variables of unknown distribution are transformed into statistics of known distribution through randomization. The test statistic checks for breaks in the structure of factor models, including changes in factor loadings and increases in the number of factors. We give the results of simulation experiments and test the factor structure of the stock return data of China’s and U.S. stock markets from January 1, 2017, to December 31, 2019. Our method performs well in both simulations and real data.