Abstract
Different ways to identify (preliminarily estimate) the impulse response function of the BoxXX1Jenkins transfer function model are discussed. The discussion is based on the situation when there are several input variables that are correlated with each other. It is found that most of the methods proposed are unsuitable, some are not reliable when there are correlated input variables, and some are expensive or difficult to use. Therefore an extension of a regression approach used by Pukkila (1980) is proposed. The new approach is based on the solution of some problems connected with the application of the regression method in our particular situation, namely the multicollinearity problem and the problem of autocorrelated residuals. It is found that the use of biased regression estimators on variables transformed with respect to the noise model should give better estimates than the usual ordinary regression estimator. To test the new approach a simulation experiment has been designed and performed. The results from the simulations indicate that the proposed method may be of value to the practitioner. It gives estimates with smaller mean squared error and lower estimated standard error.