Testing for poolability of the space-time autoregressive moving-average model

We consider the impacts of spatial aggregation on the model parameters and forecasts of the space-time autoregressive moving-average (STARMA) model. In particular, we focus on poolability, the equality of mean squared forecast error of the aggregate variable from both the non-aggregate and aggregate models, where the same model order is assumed because a model order is often unchanged under spatial aggregation, which is different from temporal aggregation. For VARMA models, there exists conditions for poolability with known parameters and a test for poolability when parameters are not known. However, this test does not apply to STARMA models due to the restricted form of their parameter matrices. In focusing on the STARMA model, we show how the aggregate model parameters are functions of the non-aggregate model parameters under poolability. In addition, we develop three poolability tests that apply to any STARMA model. We demonstrate these tests through an empirical example involving urban crime data.