ARMA model order estimation using third order cumulants

A new algorithm for estimating the order of a non-Gaussian white autoregressive moving-average (ARMA) process using third order cumulants is described. The observed data 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. The new method is based on the minimum eigenvalue of a covariance matrix derived from the observed data sequence. The derivation of this algorithm is an expansion of the algorithm proposed by Liang et al. [1993] and Liang [1992] to third order statistics. The proposed method eliminates the estimation of the ARMA model parameters. The new algorithm is applied to both ARMA and autoregressive with exogenous input (ARX) models. Simulations are provided to show that the present approach performs well even at low signal-to-noise ratios.