apca {FinTS} | R Documentation |
Asymptotic Principal Components Analysis for a fixed number of factors
apca(x,nf)
x |
a numeric matrix or other object for which 'as.matrix' will produce a numeric matrix. |
nf |
number of factors desired |
NOTE: This is a preliminary version of this function, and it may be modified in the future.
A list with four components:
eig |
eigenvalues |
factors |
estimated factor scores |
loadings |
estimated factor loadings |
rsq |
R-squared from the regression of each variable on the factor space |
Ruey Tsay
Ruey Tsay (2005) Analysis of Financial Time Series, 2nd ed. (Wiley, sec. 9.6, pp. 436-440)
# Consider the monthly simple returns of 40 stocks on NYSE and NASDAQ # from 2001 to 2003 with 36 observations. data(m.apca0103) dim(m.apca0103) M.apca0103 <- with(m.apca0103, array(return, dim=c(36, 40), dimnames= list(as.character(date[1:36]), paste("Co", CompanyID[seq(1, 1440, 36)], sep="")))) # The traditional PCA is not applicable to estimate the factor model # because of the singularity of the covariance matrix. The asymptotic # PCA provides an approach to estimate factor model based on asymptotic # properties. For the simple example considered, the sample size is # $T$ = 36 and the dimension is $k$ = 40. If the number of factor is # assumed to be 1, the APCA gives a summary of the factor loadings as # below: # apca40 <- apca(M.apca0103, 1) # # (min, 1st Quartile, median, mean, 3rd quartile, max) = # (0.069, 0.432, 0.629, 0.688, 1.071, 1.612). # # Note that the sign of any loading vector is not uniquely determined # in the same way as the sign of an eigenvector is not uniquely # determined. The output also contains the summary statistics of the # R-squares of individual returns, i.e. the R-squares measuring the # total variation of individual return explained by the factors. For # the simple case considered, the summary of R-squares is (min, 1st # Quartile, median, mean, 3rd quartile, max) = # (0.090,0.287,0.487,0.456,0.574,0.831).