Using instrumental variables for selecting the order of arma models

A methodology is developed for selecting the order of an ARMA representation of a short realization. The methodology is based on an extension of the Instrumental Variables technique and its theoretical logic is supported by the characteristic of extended Yule-Walker equations and Toeplitz matrices. The methodology is a modification of the Cormer Method and tries to identify a set of orders instead of a single order. The strength of the methodology is evaluated by comparing its numerical findings with that from the Corner Method and the Extended Sample Autocorrelation Function Method. The numerical results imply that (i) the proposed method performs, on the average better than the Corner Method and both methods outperform Extended Sample Autocorrelation Function method, and (ii) the selection of a set of orders provides more reliable results than the selection of a single order.