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Some correlation properties of spatial autoregressions

Martellosio, Federico (2009): Some correlation properties of spatial autoregressions.

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Abstract

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. An interpretation of the covariance structure of the process is provided, based on the walks connecting the spatial units. The interpretation serves to explain a number of correlation properties of SAR(1) processes, and clarifies why in practical applications it is difficult, or even impossible, to use SAR(1) processes to impose some desired correlation properties on a given data set.

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