ANew Look at the Statistical Model Identification

TLDR

Statistical hypothesis testing in time series analysis has a long history, yet the procedure is not adequately defined for statistical model identification. The authors introduce a new minimum information theoretical criterion, MAleE, designed to serve as a statistical model identification tool. MAleE is defined as the minimum of Ale ≈ (–2)log(maximum likelihood) + 2 × (number of independently adjusted parameters) for each competing model. MAleE offers a versatile, ambiguity‑free model identification procedure and its practical utility is demonstrated through numerical examples in time series analysis.

Abstract

The history of the development of statistical hypothesis testing in time series analysis is reviewed briefty and it is pointed out that the hypothesis testing procedure i. not adequately defined as the procedure for statistical model identification. The classical maximum likelihood estimation procedure is reviewed and a new estimate minimum informatioD theoretical criterion (AlC) estimate (MAleE) which is designed for the purpose of statistical identification is introduced. When there are several competing models the M.AleE is defined by the model and the maximum likelihood estimates of the parameters which give the minimum of Ale defined by Ale ~ (-2)log-(maximum likelihood) + 2(number of independently adjusted parameters within the model). MAleE provides a versatile procedure for statistical model identification which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure. The practical utllity of MAIeE in time series analysis is demonstrated with some numerical