Consider monthly simple returns of 40 stocks from NASDAQ and NYSE for years 2002 and 2003. The data are in the file m-apca40stocks.txt. The file has 40 columns. The first row of the file contains the CRSP Permno of the stocks.

(a) Perform an asymptotic principal component analysis on the 40 monthly simple stock returns with 4 common factors.

(b) Based on the scree plot, is it reasonable to use 4 common factors? If not, select an alternative number of common factors.

(c) Show the time plots of the associated loading matrix.