Asymptotically Efficient Selection of the Order by the Criterion Autoregressive Transfer Function

The autoregressive orders selected by the criterion autoregressive transfer function (CAT) of Parzen (1974), a new version, CAT^\, of CAT introduced by Parzen (1977), and the CAT₂ criterion of Bhansali (1985) are shown to be asymptotically efficient in the sense defined by Shibata (1980, 1981). A generalization of the penalty function considered by Shibata (1980) is introduced. The order selected by the CAT_\α criterion of Bhansali (1985), with any fixed \α > 1, is asymptotically efficient with respect to this generalized penalty function.