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Journal articles on the topic 'Spatial autoregressions'

Author: Grafiati
Published: 9 March 2023
Last updated: 10 March 2023

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1

Beenstock, Michael, and Daniel Felsenstein. "Spatial Vector Autoregressions." Spatial Economic Analysis 2, no. 2 (June 2007): 167–96. http://dx.doi.org/10.1080/17421770701346689.

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2

Kelley Pace, R., and Ronald Barry. "Sparse spatial autoregressions." Statistics & Probability Letters 33, no. 3 (May 1997): 291–97. http://dx.doi.org/10.1016/s0167-7152(96)00140-x.

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3

Bao, Yong, Xiaotian Liu, and Lihong Yang. "Indirect Inference Estimation of Spatial Autoregressions." Econometrics 8, no. 3 (September 3, 2020): 34. http://dx.doi.org/10.3390/econometrics8030034.

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The ordinary least squares (OLS) estimator for spatial autoregressions may be consistent as pointed out by Lee (2002), provided that each spatial unit is influenced aggregately by a significant portion of the total units. This paper presents a unified asymptotic distribution result of the properly recentered OLS estimator and proposes a new estimator that is based on the indirect inference (II) procedure. The resulting estimator can always be used regardless of the degree of aggregate influence on each spatial unit from other units and is consistent and asymptotically normal. The new estimator does not rely on distributional assumptions and is robust to unknown heteroscedasticity. Its good finite-sample performance, in comparison with existing estimators that are also robust to heteroscedasticity, is demonstrated by a Monte Carlo study.
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4

Kelley Pace, R. "Performing large spatial regressions and autoregressions." Economics Letters 54, no. 3 (July 1997): 283–91. http://dx.doi.org/10.1016/s0165-1765(97)00026-8.

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5

Martellosio, Federico. "THE CORRELATION STRUCTURE OF SPATIAL AUTOREGRESSIONS." Econometric Theory 28, no. 6 (April 27, 2012): 1373–91. http://dx.doi.org/10.1017/s0266466612000175.

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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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6

Robinson, Peter M., and Francesca Rossi. "Improved Lagrange multiplier tests in spatial autoregressions." Econometrics Journal 17, no. 1 (January 21, 2014): 139–64. http://dx.doi.org/10.1111/ectj.12025.

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7

Gupta, Abhimanyu. "ESTIMATION OF SPATIAL AUTOREGRESSIONS WITH STOCHASTIC WEIGHT MATRICES." Econometric Theory 35, no. 2 (May 3, 2018): 417–63. http://dx.doi.org/10.1017/s0266466618000142.

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We examine a higher-order spatial autoregressive model with stochastic, but exogenous, spatial weight matrices. Allowing a general spatial linear process form for the disturbances that permits many common types of error specifications as well as potential ‘long memory’, we provide sufficient conditions for consistency and asymptotic normality of instrumental variables, ordinary least squares, and pseudo maximum likelihood estimates. The implications of popular weight matrix normalizations and structures for our theoretical conditions are discussed. A set of Monte Carlo simulations examines the behaviour of the estimates in a variety of situations. Our results are especially pertinent in situations where spatial weights are functions of stochastic economic variables, and this type of setting is also studied in our simulations.
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8

Jenish, Nazgul. "SPATIAL SEMIPARAMETRIC MODEL WITH ENDOGENOUS REGRESSORS." Econometric Theory 32, no. 3 (December 18, 2014): 714–39. http://dx.doi.org/10.1017/s0266466614000905.

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This paper proposes a semiparametric generalized method of moments estimator (GMM) estimator for a partially parametric spatial model with endogenous spatially dependent regressors. The finite-dimensional estimator is shown to be consistent and root-n asymptotically normal under some reasonable conditions. A spatial heteroscedasticity and autocorrelation consistent covariance estimator is constructed for the GMM estimator. The leading application is nonlinear spatial autoregressions, which arise in a wide range of strategic interaction models. To derive the asymptotic properties of the estimator, the paper also establishes a stochastic equicontinuity criterion and functional central limit theorem for near-epoch dependent random fields.
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9

Griffith, Daniel A. "SIMPLIFYING THE NORMALIZING FACTOR IN SPATIAL AUTOREGRESSIONS FOR IRREGULAR LATTICES." Papers in Regional Science 71, no. 1 (January 14, 2005): 71–86. http://dx.doi.org/10.1111/j.1435-5597.1992.tb01749.x.

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10

Griffith, Daniel A. "Simplifying the normalizing factor in spatial autoregressions for irregular lattices." Papers in Regional Science 71, no. 1 (January 1992): 71–86. http://dx.doi.org/10.1007/bf01538661.

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11

Nguyen, Hien D., Geoffrey J. McLachlan, Jeremy F. P. Ullmann, and Andrew L. Janke. "Spatial clustering of time series via mixture of autoregressions models and Markov random fields." Statistica Neerlandica 70, no. 4 (October 12, 2016): 414–39. http://dx.doi.org/10.1111/stan.12093.

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12

Gutiérrez, David, and Rocio Salazar-Varas. "Using eigenstructure decompositions of time-varying autoregressions in common spatial patterns-based EEG signal classification." Biomedical Signal Processing and Control 7, no. 6 (November 2012): 622–31. http://dx.doi.org/10.1016/j.bspc.2012.03.004.

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13

Fingleton, Bernard. "Spatial Autoregression." Geographical Analysis 41, no. 4 (October 2009): 385–91. http://dx.doi.org/10.1111/j.1538-4632.2009.00765.x.

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14

Barbosa, S. M., M. E. Silva, and M. J. Fernandes. "Multivariate autoregressive modelling of sea level time series from TOPEX/Poseidon satellite altimetry." Nonlinear Processes in Geophysics 13, no. 2 (June 20, 2006): 177–84. http://dx.doi.org/10.5194/npg-13-177-2006.

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Abstract. This work addresses the autoregressive modelling of sea level time series from TOPEX/Poseidon satellite altimetry mission. Datasets from remote sensing applications are typically very large and correlated both in time and space. Multivariate analysis methods are useful tools to summarise and extract information from such large space-time datasets. Multivariate autoregressive analysis is a generalisation of Principal Oscillation Pattern (POP) analysis, widely used in the geosciences for the extraction of dynamical modes by eigen-decomposition of a first order autoregressive model fitted to the multivariate dataset of observations. The extension of the POP methodology to autoregressions of higher order, although increasing the difficulties in estimation, allows one to model a larger class of complex systems. Here, sea level variability in the North Atlantic is modelled by a third order multivariate autoregressive model estimated by stepwise least squares. Eigen-decomposition of the fitted model yields physically-interpretable seasonal modes. The leading autoregressive mode is an annual oscillation and exhibits a very homogeneous spatial structure in terms of amplitude reflecting the large scale coherent behaviour of the annual pattern in the Northern hemisphere. The phase structure reflects the seesaw pattern between the western and eastern regions in the tropical North Atlantic associated with the trade winds regime. The second mode is close to a semi-annual oscillation. Multivariate autoregressive models provide a useful framework for the description of time-varying fields while enclosing a predictive potential.
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15

Kyriacou, Maria, Peter C. B. Phillips, and Francesca Rossi. "Indirect inference in spatial autoregression." Econometrics Journal 20, no. 2 (June 1, 2017): 168–89. http://dx.doi.org/10.1111/ectj.12084.

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16

Bhattacharyya, B. B., J. J. Ren, G. D. Richardson, and J. Zhang. "Spatial autoregression model: strong consistency." Statistics & Probability Letters 65, no. 2 (November 2003): 71–77. http://dx.doi.org/10.1016/j.spl.2003.07.004.

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17

DUBIN, ROBIN, KELLEY PACE, and THOMAS THIBODEAU. "Spatial Autoregression Techniques for Real Estate Data." Journal of Real Estate Literature 7, no. 1 (January 1, 1999): 79–95. http://dx.doi.org/10.1080/10835547.1999.12090079.

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18

Goryainov, V. B. "M-estimates of the spatial autoregression coefficients." Automation and Remote Control 73, no. 8 (August 2012): 1371–79. http://dx.doi.org/10.1134/s0005117912080103.

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19

Ma, Chunsheng. "Spatial autoregression and related spatio-temporal models." Journal of Multivariate Analysis 88, no. 1 (January 2004): 152–62. http://dx.doi.org/10.1016/s0047-259x(03)00067-8.

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20

Goryainov, V. B. "Least-modules estimates for spatial autoregression coefficients." Journal of Computer and Systems Sciences International 50, no. 4 (August 2011): 565–72. http://dx.doi.org/10.1134/s1064230711040101.

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21

Xu, Ke, Luping Sun, Jin Liu, Xuening Zhu, and Hansheng Wang. "A spatial autoregression model with time-varying coefficients." Statistics and Its Interface 13, no. 2 (2020): 261–70. http://dx.doi.org/10.4310/sii.2020.v13.n2.a10.

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22

Goryainov, V. B. "Identification of a spatial autoregression by rank methods." Automation and Remote Control 72, no. 5 (May 2011): 975–88. http://dx.doi.org/10.1134/s0005117911050067.

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23

Long, Dan S. "Spatial autoregression modeling of site-specific wheat yield." Geoderma 85, no. 2-3 (August 1998): 181–97. http://dx.doi.org/10.1016/s0016-7061(98)00019-6.

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24

Huang, Danyang, Xiangyu Chang, and Hansheng Wang. "Spatial autoregression with repeated measurements for social networks." Communications in Statistics - Theory and Methods 47, no. 15 (October 23, 2017): 3715–27. http://dx.doi.org/10.1080/03610926.2017.1361989.

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25

Wang, Huiwen, Jie Gu, Shanshan Wang, and Gilbert Saporta. "Spatial partial least squares autoregression: Algorithm and applications." Chemometrics and Intelligent Laboratory Systems 184 (January 2019): 123–31. http://dx.doi.org/10.1016/j.chemolab.2018.12.001.

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26

Pietrzak, Michał Bernard. "Interpretation of Structural Parameters for Models with Spatial Autoregression." Equilibrium 8, no. 2 (June 30, 2013): 129–55. http://dx.doi.org/10.12775/equil.2013.010.

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The main purpose of the article is to consider a important issue of spatial econometrics, which is a proper interpretation of structural parameters of econometric models with spatial autoregression. The problem will be considered basing on the example of the spatial SAR model. Another purpose of the article is to make an overview of measures of average spatial impact proposed by the subject literature (see Lesage and Pace 2009). The analysis will include such measures as Average Total Impact to an Observation, Average Total Impact from an Observation, Average Indirect Impact to an Observation, Average Indirect Impact from an Observation and Average Direct Impact. Having considered the above issues, I will introduce a set of three original measures that allow the interpretation of the strength of the impact of the explanatory processes within the spatial SAR model, which take the forms of average direct impact, average indirect impact and average induced impact. The use of this set of measures will be illustrated with the example of the analysis of the unemployment rate in Poland. It must be emphasized that the presented set of measures may also be designated for other spatial models. With the knowledge of the empirical form of the model and of the spatial weight matrix, the set of measures introduced simplifies significantly the complex procedure of the interpretation of the structural parameters for spatial models to the use of merely three values.
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27

Peng, Xiaozhi, Hecheng Wu, and Ling Ma. "A study on geographically weighted spatial autoregression models with spatial autoregressive disturbances." Communications in Statistics - Theory and Methods 49, no. 21 (May 23, 2019): 5235–51. http://dx.doi.org/10.1080/03610926.2019.1615507.

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28

Naumov, Ilya V., and Anna Z. Barybina. "The Spatial Autoregression Model of Innovative Development of Russian Regions." Vestnik Tomskogo gosudarstvennogo universiteta. Ekonomika, no. 52 (2020): 215–32. http://dx.doi.org/10.17223/19988648/52/13.

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This work examines the spatial heterogeneity of the innovative development of regional systems and forms a spatial autoregressive model that establishes the factors of its formation and stable inter-regional relationships in innovative development. The article presents a methodological toolkit for constructing a spatial autoregressive model for the innovative development of regional systems, which involves spatial analysis of data using the segmentation of regions by the level of innovative activity and the amount of funding, provision of territories with research personnel, and development of advanced production technologies. This toolkit assumes spatial autocorrelation analysis by the Moran method using various matrices of spatial weights to find the poles of innovative growth, inter-regional spatial clusters, zones of their influence and stable inter-regional relationships in innovative development. It also assumes the formation of a spatial model describing the influence of various factors of internal and external environments on the dynamics of innovative processes. The model, features of spatial clustering of innovative processes at the macroeconomic level, and stable interregional relationships in innovative development, which were established as a result of the study, can be used to construct scenario forecasts for the innovative development of regions and search for optimal management decisions in the implementation of the Spatial Development Strategy of the Russian Federation until 2025.
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29

Liu, Kongling, Mengjun Wang, Jianchang Li, Jingjing Huang, Xuhui Huang, Shuhang Chen, and Baoquan Cheng. "Developing a Framework for Spatial Effects of Smart Cities Based on Spatial Econometrics." Complexity 2021 (June 11, 2021): 1–8. http://dx.doi.org/10.1155/2021/9322112.

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The rapid urbanization in China has already put heavy pressures on imperfect infrastructure, especially for fundamental urban functions such as power and water supply, traffic, education, and healthcare. The emergence of smart cities can help cope with the rapidly expanding demands on urban infrastructure. However, the development of smart cities in China is just in its infancy, and there is still a lack of clear understanding of the development path of smart cities. This article focuses on the development of smart cities in China. It aims to (a) judge whether there is spatial autoregression in the construction of smart cities in 83 Chinese cities and (b) identify key influencing factors in the development of smart cities in China through a spatial econometric model developed by GeoDa software. The results show that there exists spatial autoregression in the development of smart cities in China. Four key influencing factors (governmental support, innovative level, economic development, and human capital) are identified. Based on these findings, suggestions for future promoting development of smart cities in China are put forward. This research can deepen the understanding of the spatial effects of smart cities and provide valuable decision-making references for policy makers.
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30

Serkov, L. A., and K. B. Kozhov. "Interregional Distribution of Energy Potential Based on Spatial Autoregression." Zhurnal Economicheskoj Teorii 17, no. 4 (2020): 799–810. http://dx.doi.org/10.31063/2073-6517/2020.17-4.5.

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The article proposes a methodological approach for assessing the conditions of interregional interaction of Russian regions in terms of energy conditions. To this end, we substantiate and analyze the spatial distribution of Russian regions’ energy potential. An integral index of energy potential is constructed, which characterizes the main energy and economic factors of regional development in Russia. To calculate the index, we used the statistical data from the Russian Federal Statistics Service (Rosstat) and departmental organizations for 84 regions. The energy potential is calculated by using the principal component method. Interregional relationships based on this index are investigated with the help of the spatial autocorrelation method (Moran method). We focus on the relationships between the regions of the Ural Federal District and identify priority areas of energy and economic development of these territories. In particular, we analyze the spatial development of energy and economy and identify the centers where energy resources are concentrated and their spheres. Our findings can be used by state authorities and energy companies to design plans for the development of energy systems and regional economies within the framework of the Spatial Development Strategy of the Russian Federation for the Period until 2025.
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31

Bhattacharyya, B. B., G. D. Richardson, and L. A. Franklin. "Asymptotic inference for near unit roots in spatial autoregression." Annals of Statistics 25, no. 4 (August 1997): 1709–24. http://dx.doi.org/10.1214/aos/1031594738.

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32

Baran, Sándor, Gyula Pap, and Martien C. A. van Zuijlen. "Asymptotic Inference for Unit Roots in Spatial Triangular Autoregression." Acta Applicandae Mathematicae 96, no. 1-3 (March 30, 2007): 17–42. http://dx.doi.org/10.1007/s10440-007-9097-y.

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33

Mohapl, Jaroslav. "On Maximum Likelihood Estimation for Gaussian Spatial Autoregression Models." Annals of the Institute of Statistical Mathematics 50, no. 1 (March 1998): 165–86. http://dx.doi.org/10.1023/a:1003457632479.

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34

Knafl, George J., Kathleen A. Knafl, and Ruth McCorkle. "Mixed models incorporating intra-familial correlation through spatial autoregression." Research in Nursing & Health 28, no. 4 (2005): 348–56. http://dx.doi.org/10.1002/nur.20082.

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35

Ju, Yuanyuan, Yan Yang, Mingxing Hu, Lin Dai, and Liucang Wu. "Bayesian Influence Analysis of the Skew-Normal Spatial Autoregression Models." Mathematics 10, no. 8 (April 14, 2022): 1306. http://dx.doi.org/10.3390/math10081306.

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In spatial data analysis, outliers or influential observations have a considerable influence on statistical inference. This paper develops Bayesian influence analysis, including the local influence approach and case influence measures in skew-normal spatial autoregression models (SSARMs). The Bayesian local influence method is proposed to evaluate the impact of small perturbations in data, the distribution of sampling and prior. To measure the extent of different perturbations in SSARMs, the Bayes factor, the ϕ-divergence and the posterior mean distance are established. A Bayesian case influence measure is presented to examine the influence points in SSARMs. The potential influence points in the models are identified by Cook’s posterior mean distance and Cook’s posterior mode distance ϕ-divergence. The Bayesian influence analysis formulation of spatial data is given. Simulation studies and examples verify the effectiveness of the presented methodologies.
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36

Bhattacharyya, B. B., T. M. Khalil, and G. D. Richardson. "Gauss-Newton estimation of parameters for a spatial autoregression model." Statistics & Probability Letters 28, no. 2 (June 1996): 173–79. http://dx.doi.org/10.1016/0167-7152(95)00114-x.

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37

Liu, Guochang, Xiaohong Chen, Jing Du, and Kailong Wu. "Random noise attenuation using f-x regularized nonstationary autoregression." GEOPHYSICS 77, no. 2 (March 2012): V61—V69. http://dx.doi.org/10.1190/geo2011-0117.1.

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We have developed a novel method for random noise attenuation in seismic data by applying regularized nonstationary autoregression (RNA) in the frequency-space ([Formula: see text]) domain. The method adaptively predicts the signal with spatial changes in dip or amplitude using [Formula: see text] RNA. The key idea is to overcome the assumption of linearity and stationarity of the signal in conventional [Formula: see text] domain prediction technique. The conventional [Formula: see text] domain prediction technique uses short temporal and spatial analysis windows to cope with the nonstationary of the seismic data. The new method does not require windowing strategies in spatial direction. We implement the algorithm by an iterated scheme using the conjugate-gradient method. We constrain the coefficients of nonstationary autoregression (NA) to be smooth along space and frequency in the [Formula: see text] domain. The shaping regularization in least-square inversion controls the smoothness of the coefficients of [Formula: see text] RNA. There are two key parameters in the proposed method: filter length and radius of shaping operator. Tests on synthetic and field data examples showed that, compared with [Formula: see text] domain and time-space domain prediction methods, [Formula: see text] RNA can be more effective in suppressing random noise and preserving the signals, especially for complex geological structure.
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38

Zhang, Jinping, Qiuru Lu, Li Guan, and Xiaoying Wang. "Analysis of Factors Influencing Energy Efficiency Based on Spatial Quantile Autoregression: Evidence from the Panel Data in China." Energies 14, no. 2 (January 19, 2021): 504. http://dx.doi.org/10.3390/en14020504.

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This research mainly studies the factors influencing the efficiency of energy utilization. Firstly, by calculating Moran’sI and local indicators of spatial association (LISA) of energy efficiency of regions in mainland China, we found that energy efficiency shows obvious spatial autocorrelation and spatial clustering phenomena. Secondly, we established the spatial quantile autoregression (SQAR) model, in which the energy efficiency is the response variable with seven influence factors. The seven factors include industrial structure, resource endowment, level of economic development etc. Based on the provincial panel data (1998–2016) of mainland China (data source: China Statistical Yearbook, Statistical Yearbook of provinces), the findings indicate that level of economic development and industrial structure have a significant role in promoting energy efficient. Resource endowment, government intervention and energy efficiency show a negative correlation. However, the negative effect of government intervention is weakened with the increase of energy efficiency. Lastly, we compare the results of SQAR with that of ordinary spatial autoregression (SAR). The empirical result shows that the SQAR model is superior to SAR model in influencing factors analysis of energy efficiency.
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39

Martins, Emilia P. "Phylogenies, Spatial Autoregression, and the Comparative Method: A Computer Simulation Test." Evolution 50, no. 5 (October 1996): 1750. http://dx.doi.org/10.2307/2410733.

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40

Arató, M., G. Pap, and M. C. A. van Zuijlen. "Asymptotic inference for spatial autoregression and orthogonality of Ornstein-Uhlenbeck sheets." Computers & Mathematics with Applications 42, no. 1-2 (July 2001): 219–29. http://dx.doi.org/10.1016/s0898-1221(01)00146-8.

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41

Martins, Emília P. "PHYLOGENIES, SPATIAL AUTOREGRESSION, AND THE COMPARATIVE METHOD: A COMPUTER SIMULATION TEST." Evolution 50, no. 5 (October 1996): 1750–65. http://dx.doi.org/10.1111/j.1558-5646.1996.tb03562.x.

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42

Malikov, Emir, Yiguo Sun, and Diane Hite. "(Under)Mining local residential property values: A semiparametric spatial quantile autoregression." Journal of Applied Econometrics 34, no. 1 (October 4, 2018): 82–109. http://dx.doi.org/10.1002/jae.2655.

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43

Li, Hong, and Yang Lu. "COHERENT FORECASTING OF MORTALITY RATES: A SPARSE VECTOR-AUTOREGRESSION APPROACH." ASTIN Bulletin 47, no. 2 (March 23, 2017): 563–600. http://dx.doi.org/10.1017/asb.2016.37.

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AbstractThis paper proposes a spatial-temporal autoregressive model for the mortality surface, where mortality rates of each age depend on the historical values of itself (temporality) and the neighbouring ages (spatiality). The mortality dynamics is formulated as a large, first order vector autoregressive model which encompasses standard factor models such as the Lee and Carter (1992) model. Sparsity and smoothness constraints are then introduced, based on the idea that the nearer the two ages, the more important the dependence between mortalities at these ages. Our model has several novelties. First, it ensures that in the long-run, mortality rates at different ages do not diverge. Second, it provides a natural explanation of the so-called cohort effect without identifiability difficulties. Third, the model is easily extended to the multiple-population case in a coherent way. Finally, the model is associated with a closed form, non-parametric estimation method: the penalized least square, which ensures spatial smoothness of the age-dependent parameters. Using US and UK mortality data, we find that our model produces reasonable projected mortality profile in the long-run, as well as satisfying short-run out-of-sample forecast performance.
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44

Ngueyep, Rodrigue, and Nicoleta Serban. "Large-Vector Autoregression for Multilayer Spatially Correlated Time Series." Technometrics 57, no. 2 (April 3, 2015): 207–16. http://dx.doi.org/10.1080/00401706.2014.902775.

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45

Goryainov, V. B., and E. R. Goryainova. "Nonparametric identification of the spatial autoregression model under a priori stochastic uncertainty." Automation and Remote Control 71, no. 2 (February 2010): 198–208. http://dx.doi.org/10.1134/s0005117910020049.

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46

Roknossadati, S. M., and M. Zarepour. "M-estimation for near unit roots in spatial autoregression with infinite variance." Statistics 45, no. 4 (April 13, 2010): 337–48. http://dx.doi.org/10.1080/02331881003768792.

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47

Jimenez, J. C., R. Biscay, and O. Montoto. "Modeling the electroencephalogram by means of spatial spline smoothing and temporal autoregression." Biological Cybernetics 72, no. 3 (February 1995): 249–59. http://dx.doi.org/10.1007/bf00201488.

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48

Jimenez, J. C., R. Biscay, and O. Montoto. "Modeling the electroencephalogram by means of spatial spline smoothing and temporal autoregression." Biological Cybernetics 72, no. 3 (February 1, 1995): 249–59. http://dx.doi.org/10.1007/s004220050128.

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49

shen, Huaming, Meihua Xu, Feng Ran, and Liming Li. "P-5.3: A super resolution reconstruction algorithm based on spatial autoregression regularization." SID Symposium Digest of Technical Papers 49 (April 2018): 584–88. http://dx.doi.org/10.1002/sdtp.12789.

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50

Robinson, Peter M., and Francesca Rossi. "REFINED TESTS FOR SPATIAL CORRELATION." Econometric Theory 31, no. 6 (November 4, 2014): 1249–80. http://dx.doi.org/10.1017/s0266466614000498.

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Abstract:
We consider testing the null hypothesis of no spatial correlation against the alternative of pure first order spatial autoregression. A test statistic based on the least squares estimate has good first-order asymptotic properties, but these may not be relevant in small- or moderate-sized samples, especially as (depending on properties of the spatial weight matrix) the usual parametric rate of convergence may not be attained. We thus develop tests with more accurate size properties, by means of Edgeworth expansions and the bootstrap. Although the least squares estimate is inconsistent for the correlation parameter, we show that under quite general conditions its probability limit has the correct sign, and that least squares testing is consistent; we also establish asymptotic local power properties. The finite-sample performance of our tests is compared with others in Monte Carlo simulations.
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