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+// Determination of ARX parameters as described in Example 6.25 on page 203.

+// 6.15

+

+exec('armac1.sci',-1);

+exec('cra.sci',-1);

+exec('arx.sci',-1);

+exec('filt.sci',-1);

+exec('covf.sci',-1);

+exec('stem.sci',-1);

+

+process_arx = armac1([1 -0.5],[0 0 0.6 -0.2],1,1,1,0.05);

+u = prbs_a(5000,250);

+xi = rand(1,5000,'normal');

+y = arsimul(process_arx,[u xi]);

+z = [y(1:length(u))' u'];

+zd = detrend(z,'constant');

+

+// Compute IR for time-delay estimation

+[ir,r,cl_s] = cra(detrend(z,'constant'));

+

+// Time-delay = 2 samples

+// Estimate ARX model (assume known orders)

+na = 1; nb = 2; nk = 2;

+[theta_arx,cov_arx,nvar,resid] = arx(zd,na,nb,nk); 

+

+// Residual plot

+[cov1,m1] = xcov(resid,24,"coeff");

+xset('window',1); 

+subplot(2,1,1)

+stem(0:24,cov1(25:49)');xgrid();

+xtitle('Correlation function of residuals from output y1','lag');

+[cov2,m2] = xcov(resid, zd(:,2),24,"coeff");

+subplot(2,1,2)

+stem(-24:24,cov2');xgrid();

+xtitle('Cross corr. function between input u1 and residuals from output y1','lag');