The correlation structure of spatial autoregressions
Martellosio, F. (2012) The correlation structure of spatial autoregressions. Econometric Theory, 28 (6). pp. 1373-1391. ISSN 1469-4360
To link to this article DOI: 10.1017/S0266466612000175
This paper investigates how the correlations implied by a first-order simultaneous autoregressive (SAR(1)) process are affected by the weights matrix and the autocorrelation parameter. A graph theoretic representation of the covariances in terms of walks connecting the spatial units helps to clarify a number of correlation properties of the processes. In particular, we study some implications of row-standardizing the weights matrix, the dependence of the correlations on graph distance, and the behavior of the correlations at the extremes of the parameter space. Throughout the analysis differences between directed and undirected networks are emphasized. The graph theoretic representation also clarifies why it is difficult to relate properties ofW to correlation properties of SAR(1) models defined on irregular lattices.