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THE CORRELATION STRUCTURE OF SPATIAL AUTOREGRESSIONS

Published online by Cambridge University Press:  27 April 2012

Federico Martellosio
Federico Martellosio*
Affiliation:
University of Reading
*
*Address correspondence to Federico Martellosio, Department of Economics, University of Reading, Whiteknights, Reading RG6 6AA, UK; e-mail: f.martellosio@reading.ac.uk.
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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. 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 of W to correlation properties of SAR(1) models defined on irregular lattices.

Type
Miscellanea
Information
Econometric Theory , Volume 28 , Issue 6 , December 2012 , pp. 1373 - 1391
Copyright
Copyright © Cambridge University Press 2012 

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