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