ABSTRACT
Autoregressive moving average (ARMA) models are extensively used in signal processing, automatic control, and system identification to describe signals generated from a physical system. The reason is that a vast class of stationary signals can, as far as second-order moments are concerned, be described as the output of a stable rational filter, driven by white noise, i.e., these signals can be described by ARMA models. This follows from the famous theorem by Weierstrass, which implies that we can approxi mate the signal arbitrarily well by increasing the order of the filter. However, for practical reasons, it is not feasible to use models of a too high degree. Except for the computational burden it may induce, many algorithms used in signal processing become numerically unreliable as the poles and zeros of the system approach one another. The conclusion is that we must determine a finite, but not too large, order of the ARMA process. Yet the order should be chosen so that the ARMA model describes the signal under study with an accuracy that is sufficient for the application at hand.
