Detecting the order of spatial dependence via symbolic analysis

In this article, we have proposed a simple diagnostic statistical procedure for testing the order of dependence of a spatial process. The proposed test is of nonparametric nature, and it is able to deal with potential nonlinear spatial dependencies. An added value is that from a methodological point of view, the new test is based on symbolic dynamics and hence on information theory. We characterized the behavior of a symbolic entropy measure in the presence of spatial dependencies of order higher than 1. The good power performance of the new method in detecting higher order spatial lags is notable and gives rise to an expectation that it may form a suitable basis for constructive specification searches.

[1]  Symbolic dynamics , 2008, Scholarpedia.

[2]  Harold Marston Morse.  Recurrent geodesics on a surface of negative curvature , 1921 .

[3]  J. S. Huang,et al.  THE AUTOREGRESSIVE MOVING AVERAGE MODEL FOR SPATIAL ANALYSIS , 1984 .

[4]  Joris Pinkse,et al.  Those Taxes are all over the Map! A Test for Spatial Independence of Municipal Tax Rates in British Columbia , 1997 .

[5]  Luc Anselin,et al.  Under the hood , 2002 .

[6]  Gianfranco Piras,et al.  An extension of Kelejian's J-test for non-nested spatial models , 2011 .

[7]  Mariano Matilla-García,et al.  Detection of non-linear structure in time series , 2009 .

[8]  Mariano Matilla-García,et al.  Open Access Methodology Article an Entropy Test for Single-locus Genetic Association Analysis , 2022 .

[9]  A. Getis.  The Analysis of Spatial Association by Use of Distance Statistics , 2010 .

[10]  Manuel Ruiz,et al.  Testing for spatial association of qualitative data using symbolic dynamics , 2010, J. Geogr. Syst..

[11]  Sergio J. Rey,et al.  Specification Searches in Spatial Econometrics: The Relevance of Hendry's Methodology , 2003 .

[12]  M. D. Ugarte,et al.  Introduction to Spatial Econometrics , 2011 .

[13]  Mariano Matilla-García,et al.  A non-parametric test for independence based on symbolic dynamics , 2007 .

[14]  Luc Anselin,et al.  Spatial Dependence in Linear Regression Models with an Introduction to Spatial Econometrics , 1995 .

[15]  Peter Nijkamp,et al.  Diagnostic Tools for Nonlinearity in Spatial Models , 2001 .

[16]  Luc Anselin,et al.  NON‐NESTED TESTS ON THE WEIGHT STRUCTURE IN SPATIAL AUTOREGRESSIVE MODELS: SOME MONTE CARLO RESULTS* , 1986 .

[17]  D. Tj⊘stheim.  Measures of Dependence and Tests of Independence , 1996 .

[18]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[19]  Valerie Isham,et al.  Non‐Negative Matrices and Markov Chains , 1983 .

[20]  J. Eckmann,et al.  Iterated maps on the interval as dynamical systems , 1980 .

[21]  Mariano Matilla-García,et al.  Spatial Symbolic Entropy: A Tool for Detecting the Order of Contiguity , 2011 .

[22]  Minnie H. Patel,et al.  The effect of space-time demand processes on the solution of transportation problems , 1994 .

[23]  Mariano Matilla-García,et al.  A Non-Parametric Independence Test Using Permutation Entropy , 2008 .

[24]  E. Seneta.  Non-negative Matrices and Markov Chains , 2008 .

[25]  Harry H. Kelejian,et al.  A spatial J-test for model specification against a single or a set of non-nested alternatives , 2008 .

[26]  Jesús Mur,et al.  A non-parametric spatial independence test using symbolic entropy , 2010 .

[27]  J. LeSage.  Introduction to spatial econometrics , 2009 .

[28]  Luc Anselin,et al.  EFFICIENT ALGORITHMS FOR CONSTRUCTING PROPER HIGHER ORDER SPATIAL LAG OPERATORS , 1996 .

[29]  Gregory R. Grant,et al.  Bioinformatics - The Machine Learning Approach , 2000, Comput. Chem..

[30]  Sergio J. Rey,et al.  The impacts of misspecified spatial weight structures in linear regression models. , 1995 .

[31]  A. Getis,et al.  Constructing the Spatial Weights Matrix Using a Local Statistic , 2004 .

[32]  Hans J. Blommestein,et al.  Specification and estimation of spatial econometric models: A discussion of alternative strategies for spatial economic modelling , 1983 .

[33]  F. Stetzer,et al.  Specifying Weights in Spatial Forecasting Models: The Results of Some Experiments , 1982 .

[34]  L. Anselin.  Local Indicators of Spatial Association—LISA , 2010 .

[35]  J. Hadamard,et al.  Les surfaces a courbures opposees et leurs lignes geodesique , 1898 .