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The Correlation Structure Of Spatial Autoregressions

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  • Martellosio, Federico

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.

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  • Martellosio, Federico, 2012. "The Correlation Structure Of Spatial Autoregressions," Econometric Theory, Cambridge University Press, vol. 28(6), pages 1373-1391, December.
    • Handle: RePEc:cup:etheor:v:28:y:2012:i:06:p:1373-1391_00
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    Cited by:

    1. Timothy G. Conley & Sílvia Gonçalves & Min Seong Kim & Benoit Perron, 2023. "Bootstrap inference under cross‐sectional dependence," Quantitative Economics, Econometric Society, vol. 14(2), pages 511-569, May.
    2. Vainora, J., 2024. "Asymptotic Theory Under Network Stationarity," Cambridge Working Papers in Economics 2439, Faculty of Economics, University of Cambridge.
    3. Nicolás Durán & J. Paul Elhorst, 2023. "Induced earthquakes and house prices: the role of spatiotemporal and global effects," Journal of Geographical Systems, Springer, vol. 25(2), pages 157-183, April.

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