Working Papers, University of California, Department of Economics 12-17
In the ARMAX(p; r; q) model given (p; r; q); the presence of multiple parameters is often ignored. In a coprime model Hannan has shown that the unrestricted reduced form (URF) parameter is identifiable under the simple condition that the end parameter matrix has full row rank. In applications it has been found convenient to assume, without test, that the model is coprime. But in stable miniphase models, coprime or noncoprime, the incidence of multiple parameters is very real whenever the tail end transfer (impulse) coefficient matrix =URF has less than full row rank. This matrix contains the transfer matrices at lags r and q and beyond. If the timeseries process is significantly anchored in its past, =URF has full row rank and the URF parameter is unique. This is testable in large samples. The rank ofURF assists in deciding uniqueness of the URF parameter, in quantifying the common factor that generates its multiplicity and in identifying a restricted reduced form (RRF) model.