%
%    Economics 303:
%    Simulation of AR(1) process for lecture 1
%
%    George J Hall
%    Brandeis University
%    August 2006
%
close all
clear
%
%  initalize the x series
%
T = 100
x = zeros(T,1);
%
%
%
for t = 1:(T-1)
  x(t+1) = 0.95*x(t) + (round(rand)-0.5);
end

figure(1)
plot((1:T),x);
xlabel('time');
ylabel('x(t)');
title('AR(1) Simulation');

disp('i am pausing, hit the enter key to continue');
pause
 
%
%  initalize the two more series
%
y = zeros(T,1);
z = zeros(T,1);
for t = 1:(T-1)
  y(t+1) = 0.95*y(t) + (round(rand)-0.5);
  z(t+1) = 0.95*z(t) + (round(rand)-0.5);
end

figure(2)
plot((1:T),x,(1:T),y,'r',(1:T),z,'g');
xlabel('time');
ylabel('three simulated series');
title('AR(1) Simulation');