On maximum-likelihood estimation of difference equation parameters

TLDR: The article is prompted by a paper written by Liang, Wilkes and Cadzow which discussed the maximum likelihood (ML) estimation of difference equation parameters in a flawed manner and concludes that all ML-based order estimation procedures yield results that do not depend on the normalizing constraint imposed on the parameter vector.

Abstract: The article is prompted by a paper written by Liang, Wilkes and Cadzow (see ibid., vol.41, p. 3003-3009, 1993) which discussed the maximum likelihood (ML) estimation of difference equation parameters in a flawed manner. The correct ML parameter estimate is derived herein by means of a high-level argument based on the invariance principle as well as by a direct calculation. Contrary to what is suggested in the aforementioned paper, all ML-based order estimation procedures (such as AIC or GAIC rules) yield results that do not depend on the normalizing constraint imposed on the parameter vector. >