AR-order estimation by testing sets using the Modified Information Criterion

The Modified Information Criterion (MIC) is an Akaike-like criterion which allows performance control by means of a simple a priori defined parameter, the upper-bound on the error of the first kind (false alarm probability). The criterion MIC is for example used to estimate the order of Auto-Regressive (AR) processes. The criterion can only be used to test pairs of composite hypotheses; in an AR-order estimation this leads to sequential testing. Usually the Akaike criterion is used to test sets of composite hypotheses. The difference between sequential and set testing corresponds with the difference between searching the first local and the global minimum of the Akaike criterion. We extend the criterion MIC to testing a composite null-hypothesis versus a set of composite alternative hypotheses; these alternative hypotheses form a sequence where every element introduces one additional parameter. The theory is verified by simulations and is compared with the Akaike criterion used in sequential and set testing. Due to the excellent correspondence between the theory and the experimental results we consider the AR-model order estimation problem for low order AR-processes with Gaussian white noise as solved.