Eigenvalue difference test for the number of common factors in the approximate factor models

This paper proposes a new method for determining the number of common factors in the approximate factor models. Firstly, we construct a nonlinear and monotonous function of eigenvalues such that the function values of the first r largest eigenvalues are close to one and the rest are close to zero when both the number of cross-section units (N) and time series length (T) go to infinity, where r is the real value of the number of common factors. Secondly, we obtain the estimator of the number of common factors by maximizing the difference of function values of two adjacent eigenvalues arranged in descending order. Under some mild conditions, the resulting estimator can be proved to be consistent. Monte Carlo simulation study shows that the new estimator has desired performance.