Autoregressive Process Order Selection via Model-Critical Methods

The selection of the order of an autoregressive process is examined via model-critical methods that allow for constructive criticism of the data and the (tentative) model, considered jointly as a single entity. These methods yield robust estimates of the model parameters and the innovations variance, which is used in the order-selection procedure which reduces as a special case to the modified Akaike-type procedure of Hannan and Quinn. The proposed procedure selects as the order of an autoregressive process the value of that minimizes an information criterion PSIC( ) (which is a function of the model-critical parameter ( ) which governs the extent to which data and model are to be internally consistent) the model-critical estimate of the innovations variance, and the sample size. In the presence of additive outliers in the data, the model-critical procedure is superior to the Akaike and Hannan-Quinn procedures, and the superiority increases with increasing levels of contamination.