% 
% Written by:
% -- 
% John L. Weatherwax                2009-04-21
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

close all; 
clc; 
clear; 

npts = 200; 

% If alpha_x and alpha_y are of the same sign then 
% x_t and y_t seem to move in the same direction following each other
%
alpha_x = -0.2; % this ordering of signs (+/-) seems to work in that the resulting series looks very much like the one from the book
alpha_y =  0.2; 
gamma   =  1.0; 

% generate two random noise sequences: 
t = 1.0; 
epsilon_x = t * randn(1,npts); 
epsilon_y = t * randn(1,npts);

x_t = zeros(1,npts);
y_t = zeros(1,npts);
for ii=2:npts
  spread_tm1 = x_t(ii-1) - gamma * y_t(ii-1); 
  x_t(ii) = x_t(ii-1) + alpha_x * spread_tm1 + epsilon_x(ii);
  y_t(ii) = y_t(ii-1) + alpha_y * spread_tm1 + epsilon_y(ii);
end

figure; 
hx_t = plot( x_t, '-o' ); hold on; hy_t = plot( y_t, '-dr' ); title('Cointegrated Time Series'); %axis([ -10 110, -3.5, +3.5 ] ); 
legend( [ hx_t, hy_t ], {'x_t','y_t'}, 'location', 'best' ); 
if( 0 ) saveas( gcf, '../../WriteUp/Graphics/Chapter5/cointegration_example', 'eps' ); end 

% compute the spread series: 
spread = x_t - gamma * y_t; 
fprintf('mean spread= %10.6f; std spread= %10.6f\n', mean(spread), std(spread));

figure; 
plot( spread, '-o' ); title('The Spread of Two Cointegrated Time Series'); %axis([ -10 110, -3.5, +3.5 ] ); 
if( 0 ) saveas( gcf, '../../WriteUp/Graphics/Chapter5/cointegration_spread', 'eps' ); end 

return; 

% compute the spread autocorrelation function: 
sacf = acf( spread );