System Order Estimation of ARMA Models by Ladder Canonical Forms

Conventional methods for estimating the model order in system indentification, e.g., the Akaike information criterion, usually involve the maximization of some likelihood functions. In modeling autoregressive moving-average (ARMA) processes by ladder canonical forms, the ARMA process in embedded into an autoregressive (AR) ladder form and the parameters are estimated by a class of efficient least-squares algorithms that has very fast and strong convergence. Since the likelihood functions are functions of the innovations and partial correlations, which the ladder algorithms recursively compute, the embedded ARMA ladder form becomes the "natural" canonical form for the realization and computation of likelihood functions and for solving the problem of system order identification. The basic algorithm of this approach is described in this paper.