Cumulant-based order selection of non-Gaussian autoregressive moving average models: the corner method

Abstract

This paper presents a new corner location method to model order selection of an autoregressive moving average (ARMA) model. The criterion is determined in terms of the minimum eigenvalue of the third-order cumulant matrix derived from the observed data sequence. The observed sequence is modeled as the output of an ARMA system that is excited by an unobservable input, and is corrupted by zero-mean Gaussian additive noise. The system is driven by a zero-mean independent and identically distributed (i.i.d.) non-Gaussian sequence. The method is an extension to recent results based on third-order cumulant (TOC) by Al-Smadi and Wilkes. Simulations verify the performance of the proposed method even when the observed signal is heavily corrupted by additive noise. The proposed estimator, via computer simulation, is found to outperform the TOC estimator of Al-Smadi and Wilkes.