% 
% Generates ARIMA models for the yield data set.
% 
% 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; clear; rehash; clc; 

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

Y_all = load_yield_data(); n_all = length(Y_all); 

n = n_all - 3; Y = Y_all(1:n); % hold out Jan,Feb,March 1974 for testing 

fh = figure; p_data = plot( 1:n, Y, '-bx' ); axis tight; hold on; 
xlabel( 'Time' ); ylabel( 'montly difference between yeild on mortgages and on govenment loans' );
saveas( gcf, '../../WriteUp/Graphics/Chapter5/yield_data_plt', 'epsc' ); 

% plot the sample autocorrelation function ... DONE elsewhere

% plot the sample partial autocorrelation function ... DONE elsewhere

% estimate the parameters of an AR(1) model (using only the in-sample data):
[muhat,sigmahat,muci,sigmaci] = normfit(Y,0.05);
fprintf('mean estimate = %10.6f; standard error = %10.6f\n',muhat,diff(muci));

% assume a particular model based on the above plots ... AR(1) say 

% estimate the coefficients of the model (in R) ... see the file model_yield_section_5_8_2.R

% compute the one-step-ahead predicitions, z_n(1), and their residuals using the estimated 
% model coefficients
% 
%muhat = 0.97;   % ... books value 
phi   = 0.85; 
sigma = sqrt(0.024);

% Note: 
% Y_n_l(1) = y_1(1) ... and so should be compared with y(2)
% Y_n_l(2) = y_2(1) ... and so should be compared with y(3) ... etc
% 
% Y_n_l(n) = y_n(1) 
Y_n_l = muhat + phi * ( Y - muhat ); 
figure(fh); hold on; plot( 2:n, Y_n_l(1:end-1), '-rx' ); 
title( 'Raw Yield Data (in blue) and AR(1) predictions (in red)' );
saveas( gcf, '../../WriteUp/Graphics/Chapter5/yield_data_plt', 'epsc' ); 

res = Y(2:end) - Y_n_l(1:end-1); % the residuals 

% plot the sample autocorrelation function of the residuals 
plot_SACF( res );
saveas( gcf, '../../WriteUp/Graphics/Chapter5/yield_data_res_SACF', 'epsc' ); 

% compute the Portmanteau statistic Q ... skipped for time 

% compute three forecasts (and their variances) ... skipped for time