% 
% 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; 

theta_1 =  0.81;
theta_2 = -0.38; 

a = zeros(1,10);
% now 
% a(1) is a_{91} ... set to zero 
% a(2) is a_{92} ... set to zero 
% ...
% a(10) is a_{100} 
%

z = [ 15.1, 15.8, 15.9, 15.2, 15.9, 16.5, 17.1, 16.9, 17.3, 18.2 ];
% now 
% z(1) is z_{91}
% z(2) is z_{92} 
% ...
% z(10) is z_{100} 
% 

znof1 = zeros(1,10); 
% now
% znof1(1) is z_{91}(1) ... not needed or used  
% znof1(2) is z_{92}(1) ... first element filled 
% ....
% znof1(9) is z_{99}(1)
% znof1(10) is z_{100}(1) ... last element filled
%

for ii=2:9
 znof1(ii) = 2*z(ii) - z(ii-1) - theta_1 * a(ii) - theta_2 * a(ii-1);
 a(ii+1)   = z(ii+1) - znof1(ii); 
end

ii=10; % do the last point by hand (n=100) ... this is also z_{100}(1) or the first prediction from n=100
znof1(ii) = 2*z(ii) - z(ii-1) - theta_1 * a(ii) - theta_2 * a(ii-1);

z_100_l    = zeros(1,10); % <- storage ... 
z_100_l(1) = znof1(ii);   % <- computed above z_{100}(1) 

% do the rest of the predictions: first z_{100}(2) 
z_100_l(2) = 2*z_100_l(1) - z(end) - theta_2 * a(end); 

% now z_{100}(l) for l >= 3
for ll=3:10,
  z_100_l(ll) = 2*z_100_l(ll-1) - z_100_l(ll-2); 
end