%Chris House, Macro 607, Pset5
%April 9, 2008

clc;
clear;
close all;
addpath('U:\Public\html\files\matlab\functions');

y = load('GDPC96_47q1_07q4.txt');
T = size(y,1);
logy = log(y);
zero = 0*y;
date = 1947.125:0.25:2007.875;

%c)
%1.
figure;
subplot(2,1,1);
plot(date,logy,'k-');
axis([1947.125 2007.875 7 10]);
title('Log RGDP ($2000)');

%2.
mu = 1600;
[tau, F] = myHPfilter(logy,mu);
stalogy = logy - tau;
subplot(2,1,2);
plot(date,stalogy,'k-');
hold on;
plot(date,zero,'k-');
axis([1947.125 2007.875 -0.075 0.075]);
title('Log RGDP ($2000), HP filtered (\mu = 1600)');
%3.
sigma2 = std(stalogy);
sigma2text = ['\sigma^2 = ' num2str(round(sigma2*1000)/1000)];
rho = cov(stalogy(1:(T-1),1),stalogy(2:T,1))/var(stalogy(1:(T-1),1));
rhotext = ['\rho = ' num2str(round(rho(2,2)*1000)/1000)];
annotation(gcf,'textbox','FitBoxToText','off','Position',...
    [0.25 0.07 1 0.1],'LineStyle','none','String',...
    {sigma2text,rhotext});