function xxx = lect04pc
idata = load('c:\Data\USInterestRates.dat');
%figure(3);waterfall(idata)
[T,n] = size(idata);
data = idata(2:T,:)-idata(1:T-1,:);
mm = mean(data);
[pcs,comp,vars,t2] = princomp(data);
disp(' variances    % var.')
disp([vars 100*vars/sum(vars)])
% correlation graph
%figure(4);mesh(corrcoef(data))
% variances
figure(1)
pareto(100*vars/sum(vars));axis([0.5 12.5 0 100])
% factor loadings
figure(2)
subplot(3,1,1);plot(pcs(:,1));axis([0 12 -1 1])
subplot(3,1,2);plot(pcs(:,2));axis([0 12 -1 1])
subplot(3,1,3);plot(pcs(:,3));axis([0 12 -1 1])
%
pcs1  = pcs(:,1:3);  % take three loadings
comp1 = comp(:,1:3); % take three components
fitted = comp1*pcs1';
% recompose means
for i=1:size(data,2)
    fitted(:,i)=fitted(:,i)+mm(i);
end
fitted = cumsum(fitted);
for i=1:size(data,2)
    fitted(:,i)=fitted(:,i)+idata(1,i);
end
figure(5);
subplot(3,1,1)
plot(fitted(:,1),'r');hold on;
plot(idata(:,1),'g');hold off;
subplot(3,1,2)
plot(fitted(:,3),'r');hold on;
plot(idata(:,3),'g');hold off;
subplot(3,1,3)
plot(fitted(:,9),'r');hold on;
plot(idata(:,9),'g');hold off;