# 
# 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; 

% generate random noise: 
ts_mean = 0; 
ts_var  = 1.; 
npts    = 100; 
epsilon = ts_mean + sqrt(ts_var) * randn(1,npts);
figure;
plot( epsilon, '-o' ); title('white noise series'); axis([ -10 110, -3.5, +3.5 ] ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter2/random_noise', 'eps' ); 

% generate an MA(1) model: 
beta = 0.8; 
y = epsilon(2:end) + beta * epsilon(1:end-1);
figure; 
plot( y, '-o' ); title('MA(1) series'); axis([ -10 110, -3.5, +3.5 ] ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter2/ma_1_model', 'eps' ); 

% generate an AR(1) (alpha < 1) model:
alpha = 0.9; 
y = zeros(1,length(epsilon)); 
y(1) = epsilon(1);
for ii=2:length(epsilon)
  y(ii) = alpha * y(ii-1) + epsilon(ii);
end
figure; 
plot( y, '-o' ); title('AR(1) series'); %axis([ -10 110, -5.5, +5.5 ] ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter2/ar_1_model', 'eps' ); 

% generate an AR(1) random walk (alpha = 1) model:
alpha = 1.0;
y = zeros(1,length(epsilon)); 
y(1) = epsilon(1);
for ii=2:length(epsilon)
  y(ii) = alpha * y(ii-1) + epsilon(ii);
end
figure; 
plot( y, '-o' ); title('random walk series'); %axis([ -10 110, -5.5, +5.5 ] ); 
saveas( gcf, '../../WriteUp/Graphics/Chapter2/random_walk_1_model', 'eps' );