%   
% 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; clc; clear; clear functions; 

save_plots = 0; 

% calculate the correlation of these residuals:
if( exist('/home/weatherw/Trash/Poularikas/AdaptiveFilteringCode') ) addpath('/home/weatherw/Trash/Poularikas/AdaptiveFilteringCode'); end
addpath( '../Chapter4/' ); 

Y_save = load_spy_data(); n = length(Y_save); 

% take logarithmic transformation (if desired): 
%Y_save = log(Y_save); 

% consider a period of data much more recently: 
nF = 0.05*n;
Y_save = Y_save(n-nF:n); n = length(Y_save); 

% downsample our data (don't include the last two months): 
n = length(Y_save)-2*4; Y = Y_save(1:n); Y_test = Y_save( (n+1):end );

fh = figure; plot( Y, 'x-' ); 
xlabel( 'Time (weeks)' ); ylabel( 'Weekly SPY closing prices' );
if( save_plots ) saveas(gcf, '../../WriteUp/Graphics/Chapter5/spy_plt', 'epsc' ); end
axis tight; 

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); nd = length(YD); 
figure; plot( YD, 'x-' ); 
xlabel( 'Time (weeks)' ); ylabel( 'Difference in Weekly SPY closing prices' );
if( save_plots ) saveas(gcf, '../../WriteUp/Graphics/Chapter5/spy_diff_plt', 'epsc' ); end 

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

phi_kk = plot_SPACF( r_k(2:end), nd ); 
title( 'sample partial autocorrelation function of z_t-z_{t-1}' ); 
if( save_plots ) saveas( gcf, '../../WriteUp/Graphics/Chapter5/spy_diff_spacf', 'epsc' ); end 

% determine an approporite ARIMA model

% calculate the forecasts and 95% prediction intervals for the next 3 weeks closing prices