A closer look at the spatial exponential matrix specification

In this paper we analyze the partial and marginal covariance structures of the spatial model with the covariance structure based on a exponential matrix specification. We show that this model presents a puzzling behavior for many types of geographical neighborhood graphs, from the simplest to the most complex. In particular, we show that for this model it is usual to have opposite signs for the marginal and conditional correlations between two areas. We show these results through experimental examples and analytical demonstrations.