Analysis of the ∆AIC Statistic for Optimal Detection of Small Changes in Dynamic Systems

The Akaike Information Criterion (AIC) is often used as a measure of model accuracy. The ∆AIC statistic is defined by the difference between AIC values for two nested models. The ∆AIC statistic corresponding to a particular change detection problem has been shown to detect extremely small changes in a dynamic system as compared with traditional change detection monitoring procedures. In this paper, a theoretical analysis is developed that shows the ∆AIC is actually an optimal test for the detection of any small changes in the characteristics of a process. It is also shown that the change/no-change hypotheses are nested. This result leads to a generalized likelihood ratio test with optimal properties as well as the precise large sample distribution for the test. A simulation of a dynamic system with small changes demonstrates the precision of the distribution theory as compared with the empirical results.