A linear demand system within a Seemingly Unrelated Time Series Equation framework

We consider a Seemingly Unrelated Time Series Equations framework for the linear Almost Ideal Demand system. The framework is applied to a consumer demand system covering nine non-durable commodities. We test for demand homogeneity within a specification where the static linear Almost Ideal Demand system is augmented by three stochastic trends and three stochastic seasonal variables. The homogeneity restriction is rejected for about half of the commodities and in the system as a whole using conventional significance levels. However, when comparing the out-of-sample predictions from a homogeneous and non-homogeneous model, we do not find that the non-homogenous model performs better than the homogeneous one. Moreover, the income and price elasticities calculated under homogeneity restrictions are all of the right sign and have reasonable magnitudes.