What is the difference between PCA and asymptotic PCA?

Question

In two papers in 1986 and 1988, Connor and Korajczyk proposed an approach to modeling asset returns. Since these time series have usually more assets than time period observations, they proposed to perform a PCA on cross-sectional covariances of asset returns. They call this method Asymptotic Principal Component Analysis (APCA, which is rather confusing, since the audience thinks immediately of asymptotic properties of PCA).

I have worked out the equations, and the two approaches seem numerically equivalent. The asymptotics of course differ, since convergence is proved for $N \rightarrow \infty$ rather than $T \rightarrow \infty$. My question is: has anyone used APCA and compared to PCA? Are there concrete differences? If so, which ones?

Answer 1

Typically APCA gets used when there are lots of series but very few samples. I wouldn't describe APCA as better or worse than PCA, because of the equivalence you noted. They do, however, differ in when the tools are applicable. That is the insight of the paper: you can flip the dimension if it's more convenient! So in the application you mentioned, there are a lot of assets so you would need a long time series to compute a covariance matrix, but now you can use APCA. That said, I don't think APCA gets applied very often because you could try to reduce the dimensionality using other techniques (like factor analysis).