Eigenvalue Ratio Test for the Number of Factors

Eigenvalue Ratio Test for the Number of Factors

This paper proposes two new estimators for determining the number of factors in approximate factor models. We exploit the well known fact that the r eigenvalues of the variance-covariance matrix of N response variables, where r is the number of comment factors in the variables, grow unboundedly as N increases. The criterion functions used for the two estimators are related to the ratio of two adjacent eigenvalues. An important advantage of the estimators is that they do not require the use of penalty functions. The estimators can be viewed as a reformulation of the well known scree test. We show that the estimators are consistent under the general conditions of Bai and Ng (2002). Our simulation results show that the estimators have good finite sample properties unless the signal-to-noise-ratio of each factor is too low. They perform much better than the Bai-Ng estimators do when either the number of the response variables analyzed or the number of time series observations, T, is small.