Alicja Olejnik

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The aim of this paper is to introduce modern testing methods for Spatial Regression Models used for selection of the correct structure of spatial dependencies. Presented methodology allows one to test for the presence of spatial autocorrelation and at a further stage to make the correct model specification. The paper presents some merits and drawbacks of selected statistical test widely used in spatial modelling with some recommendations. The problem of spatial non-stationarity with an appropriate testing procedure is also introduced.


spatial regression models, J test, F test, Moran I, spatial non-stationarity


[1] Anselin L., (1988), Spatial Econometrics: Methods and Models, Kluwer Academic Publications, Dordrecht.

[2] Burridge P., (1980), On the Cliff–Ord Test for Spatial Correlation, Journal of the Royal Statistical Society, B, 42 (1), 107–108.

[3] Cliff A., Ord J. K., (1981), Spatial Processes: Models and Applications, Pion, London.

[4] Drukker D. M., Prucha I. R., (2013), Finite Sample Properties of the I2(q) Test Statistic for Spatial Dependence, Spatial Economic Analysis, 8, 271–292.

[5] Fingleton B., (1999), Spurious Spatial Regression: Some Monte Carlo Results with Spatial Unit Root and Spatial Cointegration, Journal of Regional Science, 39, 1–19.

[6] Godfrey L., Pesaran H., (1983), Tests of Nonnested Regression Models After Estimation by Instrumental Variables or Least Squares, Journal of Econometrics, 21, 133–154.

[7] Kelejian H. H., (2008), A Spatial Test J for Model Specifi cation Against a Single or a Set of Non–Nested Alternatives, Letters in Spatial and Resource Sciences, 1 (1), 3–11.

[8] Kelejian H. H., Prucha I. R., (2001), On the Asymptotic Distribution of the Moran I Test Statistic with Applications, Journal of Econometrics, 104, 219–257.

[9] Kosfeld R., Lauridsen J., (2004), Dynamic Spatial Modeling of Regional Convergence Processes, Empirical Economics, 29, 705–722.

[10] Kosfeld R., Lauridsen J., (2006), A Test Strategy for Spurious Regression, Spatial Nonstationarity, and Spatial Cointegration, Papers in Regional Science, 85 (3), 363–377.

[11] Lauridsen J., (1999), Spatial Cointegration Analysis in Econometric Modelling, ERSA conference papers ersa99pa181, European Regional Science Association.

[12] Moran P., (1950), Notes on Continuous Stochastic Phenomena, Biometrika, 37, 17–23.

[13] Olejnik A., (2008), Using the Spatial Autoregressively Distributed Lag Model in Assessing the Regional Convergence of per–capita Income in the EU25, Papers in Regional Science, 87 (3), 371–384.

[14] Olejnik A., (2013), Spatial Autoregressive Model – a Multidimensional Perspective with an Example Study of the Spatial Income Process in the EU 25, PREPARE, working papers, wysłane do recenzji do Geographical Analysis.

[15] Pesaran H., Weeks M., (2001), Nonnested Hypothesis Testing: An Overview, w: Baltagi B., (red.), A Companion to Theoretical Econometrics, Blackwell, Oxford.

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