% 
% Written by:
% -- 
% John L. Weatherwax                2009-04-21
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

close all; drawnow; clear functions; 
rehash; 
clc; 

if( exist('/home/weatherw/Trash/Poularikas/AdaptiveFilteringCode') ) addpath('/home/weatherw/Trash/Poularikas/AdaptiveFilteringCode'); end
addpath( '../Chapter2/' ); 
addpath( '../Chapter4/' ); % plot_SACF.m

Y = load_master_card_applications(); 

fh = figure; plot( Y, 'x-' ); 
xlabel( 'Month starting from Januwary 1967' ); ylabel( 'MC applications' ); 
saveas(gcf, '../../WriteUp/Graphics/Chapter5/mca_plt', 'epsc' ); 

% stabalize the variance with a logorithmic transform: 
Y = log(Y); 

fh = figure; plot( Y, 'x-' ); 
xlabel( 'Month starting from Januwary 1967' ); ylabel( 'Log MC applications' ); 
saveas(gcf, '../../WriteUp/Graphics/Chapter5/log_mca_plt', 'epsc' ); 

fprintf('s^2(Y)= %10.6f, s^2(diff(Y))= %10.6f, s^2(diff(Y,2))= %10.6f, s^2(diff(Y,3))= %10.6f\n',var(Y),var(diff(Y)),var(diff(Y,2)),var(diff(Y,3)))

% non-statonary ... take first differences and plot: 
YD = diff(Y); 
figure; plot( YD, 'x-' ); 
xlabel( 'Month starting from Januwary 1967' ); ylabel( 'MC applications' ); 
saveas(gcf, '../../WriteUp/Graphics/Chapter5/mca_diff_plt', 'epsc' ); 

r_k = plot_SACF( YD );
title( 'sample autocorrelation function of z_t-z_{t-1}' ); 
saveas(gcf, '../../WriteUp/Graphics/Chapter5/mca_diff_z_t_sacf', 'epsc' ); 

phi_kk = plot_SPACF( r_k(2:end), nd ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter5/mca_diff_spacf', 'epsc' ); 

% find an approporiate model ... use an MA(1) model ... see the R script prob_5_24.R 

theta = 0.6666;
sigma = sqrt(0.04553); 

% derive predictions for the next four months ... done in the associated *.R file