How can I interpret the results of a simulation of ARX process in Matlab? -

How can I interpret the results of a simulation of ARX process in Matlab? -

i simulated the next commands:

process_arx= idpoly([1 -0.5],[0 0 0.6 -0.2],1,1,1,'noisevariance',0.05,'ts',1); uk=idinput(2555,'prbs',[0 0.2], [-1 1]); yk=sim(process_arx,uk,'noise');

and first 10 of uk , yk are:

[uk(1:10) yk(1:10)] ans = -1.0000 0.1202 -1.0000 0.4702 -1.0000 -0.8700 -1.0000 -0.6422 -1.0000 -0.6498 -1.0000 -1.0173 -1.0000 -1.0056 -1.0000 -0.8262 -1.0000 -0.0129 -1.0000 0.2128

as far understand doing simulating next equation:

y(t)= 0.5*y(t-1) + 0.6*u(t-2) -0.2*u(t-3)

so example, if want y(4), have calculate : y(4)=0.5*y(3) + 0.6*u(2) -0.2*u(1)

from values : y(3)= -0.87 ; u(2)= -1 , u(1) = -1

y(4) should -0.835 , simulation gave me -0.6422 !

how can interpret correctly simulation result?

i think don't take business relationship model innovations e(t) stochastic, i.e.

y(t)= 0.5*y(t-1) + 0.6*u(t-2) -0.2*u(t-3) + e(t)

matlab simulation differential-equations