About the underlying principle of the function "predict"

I have read many books on the theory of time series forecast and system identification. But I still cannot find the formulas that the function "predict" follows in Matlab. The result by either optimal prediction or kalman filter is different from that function. So can anybody tell me the formulas or the reference book?

Thanks in advance.

Answer 1

[Rajiv Singh]

The prediction is based on computing a kalman filter. See chapter 3 in "System Identification, Theory for the User", 2nd ed, Lennart Ljung.

Could you post an example of the difference you are observing?

[zh]

Thank you for your attention. I have solve my problem. For stationary ARMA process, the function "predict" is just k-step ahead optimal forecast. Actually, the formulas are very simple. I have got the same result as the function producing.