On determination of the number of factors in an approximate factor model

Abstract

This paper proposes a ridge-type method for determining the number of factors in an approximate factor model. The new estimator of factor number is obtained by maximizing both the ratio of two adjacent eigenvalues and the cumulative contribution rate of the factors which represents the explanatory power of the common factors for response variables. Our estimator is proved to be as asymptotically consistent as those in (Ahn, S., and A. Horenstein. 2013. “Eigenvalue Ratio Test for the Number of Factors.” Econometrica 81: 1203–27). But Monte Carlo simulation experiments show our method has better correct selection rates in finite sample cases. A real data example is given for illustration.