%
% ex3.m is an example matlab program 
%

% ----- save output to file ----- %

clear all
diary ex3.mout
diary off
delete ex3.mout
diary ex3.mout

% ----- display date and time of computation ----- %

format bank
date
time0 = clock;

% ----- find mean of system ----- %

A0 = [0.9 0 2;
      1 0 0 ;
      0 0 1 ];

[mux D] = eig(A0) 

mux = mux(:,3);

% ----- now simluate the series ----- %

% - generate random vector - %

w = randn(1,1000);

x(:,1) = mux ;


C = [1;0;0];

for j = 1:999
 x(:,j+1) = A0*x(:,j)+C*w(:,j+1) ;
end



% ----- simulate state space system ----- %
% - set series length - %

iter = 100;

% ----- enter matrices and initial values ----- %

A0 = [-0.8 0.1 0.01;
       1 0 0 ;
       0 0 1 ];

C = [1;
     0;
     0];

G = [ 1 0 0;
     .2 0 0 ];

% - compute first moments - %

[mux D] = eig(A0) 

% - generate random shocks - %

w = randn(1,iter+1);

% - iterate to generate series - %

x = [zeros(2,iter+1) ;
     ones(1,iter+1) ] ;

for j = 1:100
 x(:,j+1) = A0*x(:,j)+C*w(:,j+1);
end


% - compute y's - %

for j = 1:100
 y(:,j) = G*x(:,j);
end;

% ----- alternative system ----- %

A0 = [0];
C = [1];

% - generate random shocks - %

w = randn(1,iter+1);

% - iterate to generate series - %

x = zeros(1,iter+1);

for j = 1:100
 x(:,j+1) = A0*x(:,j)+C*w(:,j+1);
end

x'

% ----- compute first and second moments ----- %

alpha = 10*(1-1.2+.3)

A = [ 1.2 -.3 0 0 alpha; 
      1 0 0 0 0;
      0 1 0 0 0;
      0 0 1 0 0;
      0 0 0 0 1 ]

C = [1; 0; 0; 0; 0]

[mux D] = eig(A) 

Cx      = doublej(A,C*C')

% ----- turn off diary ----- %

comptime = etime(clock, time0)
diary off