Asymptotic inference for near unit roots in spatial autoregression

Bhattacharyya, B. B.; Richardson, G. D.; Franklin, LeRoy A.

doi:10.1214/aos/1031594738

Cited by 18 publications

(12 citation statements)

References 20 publications

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“…1 In some noneconomic fields, such as image analysis and agriculture, it is well established that simultaneous or conditional autoregressions often lead to a very large value of the autocorrelation parameter (e.g., Besag and Kooperberg, 1995;Bhattacharyya et al, 1997). When data are observed over a regular lattice, this is usually interpreted as an indication of a type of nonstationarity similar to that due to near unit roots in time series.…”

Section: The Testing Problemmentioning

confidence: 99%

Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression

Martellosio

2009

Econom. Theory

153

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This paper derives some exact power properties of tests for spatial autocorrelation in the context of a linear regression model. In particular, we characterize the circumstances in which the power vanishes as the autocorrelation increases, thus extending the work of Krämer (2005, Journal of Statistical Planning and Inference 128, 489-496). More generally, the analysis in the paper sheds new light on how the power of tests for spatial autocorrelation is affected by the matrix of regressors and by the spatial structure. We mainly focus on the problem of residual spatial autocorrelation, in which case it is appropriate to restrict attention to the class of invariant tests, but we also consider the case when the autocorrelation is due to the presence of a spatially lagged dependent variable among the regressors. A numerical study aimed at assessing the practical relevance of the theoretical results is included.

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Section: The Testing Problemmentioning

confidence: 99%

Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression

Martellosio

2009

Econom. Theory

153

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“…Spatial unit roots have also been analyzed in the case of SAR processes on regular ACCEPTED MANUSCRIPT lattices; see, e.g., Bhattacharyya et al (1997), Baran et al (2004) andPaulauskas (2007).…”

Section: Introductionmentioning

confidence: 99%

Efficiency of the OLS estimator in the vicinity of a spatial unit root

Martellosio

2011

Statistics & Probability Letters

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“…The doubly geometric model was the first one for which the nearly unstability has been studied. Bhattacharyya et al [8] showed that in the case when a sequence of stable models with α n → 1, β n → 1 was considered, in contrast to the AR(1) model, the sequence of Gauss-Newton estimators ( α n , β n ) of (α n , β n ) were asymptotically normal, namely,…”

Section: Introductionmentioning

confidence: 99%

On the least squares estimator in a nearly unstable sequence of stationary spatial AR models

Baran

Pap

2009

Journal of Multivariate Analysis

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a b s t r a c tA nearly unstable sequence of stationary spatial autoregressive processes is investigated, when the sum of the absolute values of the autoregressive coefficients tends to one. It is shown that after an appropriate normalization the least squares estimator for these coefficients has a normal limit distribution. If none of the parameters equals zero then the typical rate of convergence is n.

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Asymptotic inference for near unit roots in spatial autoregression

Cited by 18 publications

References 20 publications

Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression

Power Properties of Invariant Tests for Spatial Autocorrelation in Linear Regression

Efficiency of the OLS estimator in the vicinity of a spatial unit root

On the least squares estimator in a nearly unstable sequence of stationary spatial AR models

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