A note on identification of multivariate time-series models

We analyze some of the difficulties of identifying multivariate time-series models with feedback, when carried through the two-stage procedure as in Haugh-Box (1977). We find that if the procedure is simplified, as in Jenkins (1979), the identified model can be seriously misspecified. When the procedure is applied correctly, it becomes extremely complicated, as in Granger-Newbold (1977). In such cases, there is a serious risk of overparametrization. The complication is mostly caused by the underlying structure of the multivariate model for the univariate innovations which can be considerably more complicated than the multivariate time-series model of interest.