Traditionally, restrictions on systems of demand equations have been tested using static models, whilst being estimated with time series data. This paper develops a vector time series model of expenditure shares in the context of a singular dynamic demand system. The model allows for non-symmetric and non-homogeneous short run behaviour. The homogeneity and symmetry restrictions are only examined in the long run structure. Results based on Canadian time series data are presented and reject the current practise of static modelling while restrictions suggested by economic theory are not rejected when imposed on the long run structure.