Identification of the multi-input box-Jenkins transfer function model

In this paper different ways to identify the order of the Box–Jenkins transfer function model are discussed. The discussion concerns estimation of the impulse response weight function in the case of more than one input variable. It is found that most of the existing methods are either unsuitable when there is more than one input variable, or expensive or difficult to use. To overcome these deficiencies an extended regression method is proposed. The new method is based on the solution of some problems in connection with the use of the regression method. The impulse response weights are estimated by a biased regression estimator on variables transformed with respect to the noise model. To test the new approach a small simulation experiment has been performed. The results from the simulations indicate that the proposed method may be of value to the practitioner.