The correlation structure of spatial autoregressions
- Publisher: Cambridge University Press
This paper investigates how the correlations implied by a first-order simultaneous\ud autoregressive (SAR(1)) process are affected by the weights matrix and the autocorrelation\ud parameter. A graph theoretic representation of the covariances in terms of\ud walks connecting the spatial units helps to clarify a number of correlation properties\ud of the processes. In particular, we study some implications of row-standardizing\ud the weights matrix, the dependence of the correlations on graph distance, and the\ud behavior of the correlations at the extremes of the parameter space. Throughout\ud the analysis differences between directed and undirected networks are emphasized.\ud The graph theoretic representation also clarifies why it is difficult to relate properties\ud ofW to correlation properties of SAR(1) models defined on irregular lattices.