##################################################################
#
#  EXCHANGE RATE DATA
#  West & Harrison (1997, 16.4.6 Application to exchange 
#  rate modelling, pages 612-615).
#  Series:  
#      US Dollar
#      Canadian Dollar
#      Japanese Yen
#      French Franc
#      Italian Lira and Deutschmark.
#  
#  Periodicity: Monthly data from January 1971 to December 1986.
#
##################################################################

names = c("US Dollar","Canadian Dollar","Japanese Yen",
          "French Franc","Italian Lira","Deutschmark")
n     = 144
p     = 6
y     = matrix(scan("exchangerate-monthly.txt"),n,p,byrow=T)


pdf(file="exrate.pdf",width=9,height=5)
par(mfrow=c(2,3))
for (i in 1:p){
  plot(y[,i],xlab="months",ylab="",main=names[i],axes=F,type="l")
  axis(2)
  axis(1,at=seq(1,n,by=12),label=1975:1986)
}
dev.off()

r = exp(apply(log(y),2,diff))-1

pdf(file="exrate-return.pdf",width=9,height=5)
par(mfrow=c(2,3))
for (i in 1:p){
  plot(r[,i],xlab="months",ylab="",main=names[i],
       axes=F,type="l",ylim=range(r))
  axis(2)
  axis(1,at=seq(12,n-1,by=12),label=1976:1986)
  abline(h=0,col=2)
}
dev.off()

round(cor(y),2)
round(cov(y),3)
      [,1]  [,2]  [,3]  [,4]  [,5]  [,6]
[1,]  1.00  0.86  0.80 -0.45 -0.50  0.62
[2,]  0.86  1.00  0.43 -0.14 -0.07  0.29
[3,]  0.80  0.43  1.00 -0.45 -0.65  0.87
[4,] -0.45 -0.14 -0.45  1.00  0.92 -0.11
[5,] -0.50 -0.07 -0.65  0.92  1.00 -0.38
[6,]  0.62  0.29  0.87 -0.11 -0.38  1.00
       [,1]   [,2]       [,3]    [,4]       [,5]    [,6]
[1,]   0.119  0.098     31.076  -0.199    -65.349   0.122
[2,]   0.098  0.110     16.037  -0.061     -9.395   0.056
[3,]  31.076 16.037  12678.481 -63.930 -27804.494  56.056
[4,]  -0.199 -0.061    -63.930   1.624    444.863  -0.078
[5,] -65.349 -9.395 -27804.494 444.863 143476.615 -82.633
[6,]   0.122  0.056     56.056  -0.078    -82.633   0.327


fac2 = factanal(y,2,"mle",score="regression")

fac2$loadings

    Factor1 Factor2
[1,]  0.938  -0.341 
[2,]  0.946   0.093      
[3,]  0.650  -0.546 
[4,] -0.156   0.908 
[5,] -0.177   0.982 
[6,]  0.548  -0.289 

fac2$uniq
[1] 0.00500000 0.09543247 0.28028025 0.15210142 0.00500000
[6] 0.61608539


fac2$loadings^2