How to find a system response of armax model for other data set? What e(t) in the system model?

Discrete-time ARMAX model: A(z)y(t) = B(z)u(t) + C(z)e(t) A(z) = 1 - 2.916 z^-1 + 2.84 z^-2 - 0.9237 z^-3

B1(z) = 0.0004539 - 0.002285 z^-1                       

B2(z) = -1.451e-05 - 1.763e-05 z^-1                     

B3(z) = -0.00468 + 0.004787 z^-1                        

C(z) = 1 + 0.7955 z^-1 + 0.795 z^-2 + 0.998 z^-3

In the above function, what is e(t)? How to find y(t) for new data set (testing purpose)?

Answer 1

e(t) is noise disturbance or also called innovations terms. Usually assumed to be white noise. Once you have the estimated model supply your u(t) and look at the response, its just like any regular transfer function.

Answer 2

Finding values of y(t) for a given u(t) is simulation. Use the SIM command: http://www.mathworks.com/help/ident/ref/sim.html

Simulation will assume zero values for innovations e(t). If you need to predict K-step head values of y(t) using past measurements of (u,y), use PREDICT http://www.mathworks.com/help/ident/ref/predict.html

See http://www.mathworks.com/help/ident/simulation-and-prediction.html for more information on simulation and prediction.