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Determining the number of factors is essential to factor analysis. In thispaper, we propose {an efficient cross validation (CV)} method to determine thenumber of factors in approximate factor models. The method applies CV twice,first along the directions of observations and then variables, and hence isreferred to hereafter as double cross-validation (DCV). Unlike most CV methods,which are prone to overfitting, the DCV is statistically consistent indetermining the number of factors when both dimension of variables and samplesize are sufficiently large. Simulation studies show that DCV has outstandingperformance in comparison to existing methods in selecting the number offactors, especially when the idiosyncratic error has heteroscedasticity, orheavy tail, or relatively large variance.

Double Cross Validation for the Number of Factors in Approximate Factor Models