% 
% 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; 

r_k  = [ 1, -0.32, 0.2, 0.05, -0.06, -0.08 ]; n_r_k = length(r_k); n = 100; 
sf=figure; stem( 0:(n_r_k-1), r_k, 'markerfacecolor', 'b' );  
xlabel( 'lag (k)' ); ylabel('r_{a}(k)');

se_r_k = 1.0 / sqrt(n); % plot the value of the standard errors of the sample autocorrelations: 

figure(sf); hold on; plot( 0:(n_r_k-1), -2*se_r_k*ones(n_r_k,1), 'r-' ); 
figure(sf); hold on; plot( 0:(n_r_k-1), +2*se_r_k*ones(n_r_k,1), 'r-' ); axis tight; 

saveas( gcf, '../../WriteUp/Graphics/Chapter5/prob_5_9_a_k', 'epsc' ); 

% plot the sample partial autocorrelation function: 
%
phi_kk = spacf(r_k(2:end)); n_r_k = length(phi_kk); 

sf=figure; stem( 1:n_r_k, phi_kk, 'markerfacecolor', 'b' );  
xlabel( 'lag (k)' ); ylabel('\phi_{kk}');

se_r_k = 1.0 / sqrt(n); % plot the value of the standard errors of the sample autocorrelations: 

figure(sf); hold on; plot( 1:(n_r_k), -2*se_r_k*ones(n_r_k,1), 'r-' ); 
figure(sf); hold on; plot( 1:(n_r_k), +2*se_r_k*ones(n_r_k,1), 'r-' ); 

saveas( gcf, '../../WriteUp/Graphics/Chapter5/prob_5_9_phi_a_k', 'epsc' );