On estimating ARMA model orders

In system identification where a given sequence represents the output of an autoregressive moving-average (ARMA) process, the estimation of the proper ARMA model order and parameters is an important problem. In this paper, we propose a method for estimating the orders of an ARMA process from the observations of the noise-corrupted output using third order cumulants. The observed sequence is modeled as the output of an ARMA system that is excited by an unobservable input, and is corrupted by white, zero-mean additive Gaussian noise. This method is based on the minimum eigenvalue of a covariance matrix derived from the observed data sequence. This is a generalization of the approach of Liang et al. [1,2], which eliminates the estimation of the a_i and b_i coefficients