Automatic identification of ARMA systems

Abstract

Autoregressive moving-average (ARMA) system identification with only output measurements is a well-known problem in various science and engineering areas such as spectral estimation and speech processing. Although this problem is an ‘old’ problem and widely considered to be solved, recent algorithms and results by Al-Smadi and Wilkes and Al-Smadi indicate that this is far from the actual case. In fact the much higher accuracy of these new algorithms calls for re-examination of this important problem. The objective of this article is to propose an automated procedure for selecting the model order and estimating the parameters of the ARMA system from third order cumulants (TOC) of the contaminated observations of the output data. The system is driven by a zero-mean independent and identically distributed (i.i.d.) sequence. The driving input is non-Gaussian and is not observed.