%
% ex2.m is an example matlab program 
%

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

clear all
diary ex2.mout
diary off
delete ex2.mout
diary ex2.mout

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

format long
date
time0 = clock;

% ----- compute standardized eigenvalues ---- %
 
P = [.9 .1 ;
     .3 .7];
 
[V,D] = eig(P') 
 
% - standardize - %
 
pii = [ V(1,1)/(V(1,1)+V(2,1));
       V(2,1)/(V(1,1)+V(2,1))]

% ----- compute the infinite sum from hw1 question 2f ----- %

P1 = [.9 .1 ; .3 .7];
y1 = [1;5];

temp1 = y1;
beta1 = .9;

% - construct a "do" loop - %

for j = 1:1000
 temp1 = temp1 + beta1^(j)*P1^(j)*y1;
end;

temp2 = inv(eye(2)-beta1*P1)*y1;

% - print two methods - %

temp1, temp2

% ----- simulate a markov chain using sargents code ----- %

P = [.9 .1 ;
     .3 .7];

mp = markov(P,100,1,[1 2])'

% - augment mp to include first obs - %

mp = [1 ; mp ]

% ----- generate y from x ----- %

ybar = [ -1; 1]

for j = 1:100
 y(j,1) = ybar( mp(j,1),1) ;
end

% - print y - %

y

% ----- evaluate the likelihood of this event occuring ----- %

L = pii(mp(1,1),1) ;

for j = 2:100
 L = L*P(mp(j-1,1),mp(j,1)); 
end;

% - print likelihood - %

L

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

comptime = etime(clock, time0)
diary off