In this paper we address the question of how to derive a statistically well-defined empirical model and the closely related question of how to choose the observational variables. Since the data are nonstationary, the derived empirical model is based on the multivariate cointegration model. The autoregressive and the moving average form of this model are discussed in terms of long run relations and common trends driving the system with reference to Australian money demand data. The importance of correct specification of linear trends in the model is demonstrated. The testing of structural hypotheses is found to greatly facilitate the interpretation of the two-dimensional cointegration space and finally leads to a formulation of two cointegration relations which can be interpreted as reasonable proxies for "excess money" and "excess aggregate demand" respectively. For the money relation long run price and income homogeneity is tested and accepted.