Working paper

About predictions in spatial autoregressive models

Christine Thomas-Agnan, Thibault Laurent, and Michel Goulard


We address the problem of prediction in the spatial autoregressive SAR model for areal data which is classically used in spatial econometrics. With the Kriging theory, prediction using Best Linear Unbiased Predictors is at the heart of the geostatistical literature. From the methodological point of view, we explore the limits of the extension of BLUP formulas in the context of the spatial autoregressive SAR models for out-of-sample prediction simultaneously at several sites. We propose a more tractable \almost best" alternative and clarify the relationship between the BLUP and a proper EM-algorithm predictor. From an empirical perspective, we present data-based simulations to compare the efficiency of the classical formulas with the best and almost best predictions.


Spatial simultaneous autoregressive models; out of sample prediction; best linear unbiased prediction;

Replaced by

Michel Goulard, Thibault Laurent, and Christine Thomas-Agnan, About predictions in spatial autoregressive models : Optimal and almost optimal strategies, Spatial Economic Analysis, vol. 12, n. 2-3, April 2017, pp. 304–325.

See also

Published in

TSE Working Paper, n. 13-452, December 18, 2013, revised December 2016