% Set up the model for simulation
  arma_mod = idpoly(1,0,[1 -0.3],[1 -0.8 0.3],1,1);

% Generate the inputs for simulation
% Deterministic Input can be anything
  u = zeros(2048,1); 
  e = randn(2048,1);

% Simulate the model
  y = idsim(arma_mod,[u e]);

% Plot ACF and PACF for 10 lags
  figure, plotacf(y,1e-03,11,1); 
  figure, pacf(y,10);

% Estimate AR(1) model and present it
  mod_est1 = armax(y,[1 0]); present(mod_est1)

% compute the residuals
  err_mod1 = pe(mod_est1,y);

% Plot ACF and PACF for 10 lags
  figure
  plotacf(err_mod1,1e-03,11,1); 
  figure, pacf(err_mod1,10);

% Check ACF and PACF of residuals 
  mod_est2 = armax(y,[1 1]); present(mod_est2)
  err_mod2 = pe(mod_est2,y);

% Plot ACF and PACF for 10 lags
  figure
  plotacf(err_mod2,1e-03,11,1); 
  figure, pacf(err_mod2,10);