%ECON 607 Problem Set 1, Question 3
%Andrew McCallum, Jan. 23, 2008

%Clear memory, screen, and close all graphs before execution.
clear all;
clc;
close all;

%a)
%Adds the path where I store my functions.
addpath('U:\Public\html\files\matlab\functions');

%c)
%4
alpha = 0;
sig2 = 1;
T = 1100;
y0 = 1;
repeat = 100;

%AR(1) process with rho: 
rho = 0.95;
%note that rho must be less than one or you will get an explosive series
%set the seed so we all get the same results
randn('seed',1234);
%generate the ar1 using our cute little ar1 program. notice that we can
%generate an TxRepeat matrix of ar1 process if we want .
yburn = genar1(alpha, rho, sig2, T, y0, repeat);
%keep the last 100 observations of each process
y = yburn(T-99:T,1:repeat);
rhohat95 = 9999*ones(repeat,1); 
for p = 1:1:100
    [rhohat95(p,1), junk, junk2, junk3] = myols(y(2:100,p),y(1:99,p));
end
murhohat95 = round(100*mean(rhohat95))/100;
figure(1);
subplot(2,2,1);
hist(rhohat95);
title(['\rho = 0.95; \mu =',num2str(murhohat95)]);
%change the color of the inside of the boxes to white
h95 = findobj(gca,'Type','patch');
set(h95,'FaceColor','w');

%AR(1) process with rho: 
rho = 0.5;
%note that rho must be less than one or you will get an explosive series
%set the seed so we all get the same results
randn('seed',1234);
%generate the ar1 using our cute little ar1 program. notice that we can
%generate an TxRepeat matrix of ar1 process if we want .
yburn = genar1(alpha, rho, sig2, T, y0, repeat);
%keep the last 100 observations of each process
y = yburn(T-99:T,1:repeat);
rhohat5 = 9999*ones(repeat,1); 
for p = 1:1:100
    [rhohat5(p,1), junk, junk2, junk3] = myols(y(2:100,p),y(1:99,p));
end
murhohat5 = round(100*mean(rhohat5))/100;
figure(1);
subplot(2,2,2);
hist(rhohat5);
title(['\rho = 0.5; \mu =',num2str(murhohat5)]);
%change the color of the inside of the boxes to white
h5 = findobj(gca,'Type','patch');
set(h5,'FaceColor','w');

%AR(1) process with rho: 
rho = 0.999;
%note that rho must be less than one or you will get an explosive series
%set the seed so we all get the same results
randn('seed',1234);
%generate the ar1 using our cute little ar1 program. notice that we can
%generate an TxRepeat matrix of ar1 process if we want .
yburn = genar1(alpha, rho, sig2, T, y0, repeat);
%keep the last 100 observations of each process
y = yburn(T-99:T,1:repeat);
rhohat999 = 9999*ones(repeat,1); 
for p = 1:1:100
    [rhohat999(p,1), junk, junk2, junk3] = myols(y(2:100,p),y(1:99,p));
end
murhohat999 = round(100*mean(rhohat999))/100;
figure(1);
subplot(2,2,3);
hist(rhohat999);
title(['\rho = 0.5; \mu =',num2str(murhohat999)]);
%change the color of the inside of the boxes to white
h999 = findobj(gca,'Type','patch');
set(h999,'FaceColor','w');