Gauss-Newton estimation of parameters for a spatial autoregression model

Bhattacharyya, B. B.; Khalil, Magdy T.; Richardson, G. D.

doi:10.1016/0167-7152(95)00114-x

Cited by 19 publications

(11 citation statements)

References 13 publications

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“…Corollary 2 follows applying (9) to (8), while, for the proof of Corollary 3, we note that, for model (5) with the boundary conditions Y in = 0 for all i, we have…”

Section: Proofsmentioning

confidence: 99%

See 1 more Smart Citation

On unit roots for spatial autoregressive models

Paulauskas

2007

Journal of Multivariate Analysis

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In this paper we consider the unit root problem for one rather simple autoregressive model Y t,s =aY t−1,s + bY t,s−1 +ε t,s on a two-dimensional lattice. We show that the growth of variance of Y t,s is essentially different from corresponding growth in the unit root case for AR(1) or AR(2) time series models. We also show that the dimension of the lattice plays an important role: the growth of variance of autoregressive field on a d-dimensional lattice is different for d = 2, 3 and d 4.

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“…Corollary 2 follows applying (9) to (8), while, for the proof of Corollary 3, we note that, for model (5) with the boundary conditions Y in = 0 for all i, we have…”

Section: Proofsmentioning

confidence: 99%

“…can be considered as being more simple one, see the recent papers [5,6] and references therein. The reason is that this model can be reduced to two "one-dimensional" autoregressions.…”

Section: Introductionmentioning

confidence: 99%

On unit roots for spatial autoregressive models

Paulauskas

2007

Journal of Multivariate Analysis

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“…Since the initial work on spatial statistical models developed in [3,4,16,[18][19][20][21][33][34][35], among others, the spatial series modeling framework has been widely considered in several applied fields such as geology, geophysics, biology, agriculture, spatial econometrics, image processing, etc. This framework is useful when data are collected on a regular grid.…”

Section: Introductionmentioning

confidence: 99%

Spatial autoregressive and moving average Hilbertian processes

Ruiz-Medina

2011

Journal of Multivariate Analysis

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“…Namely, since the initial work on spatial statistical models developed in Basu and Reinsel [3], Bhattacharyya, Khalil and Richardson [5], Güyon [17], Jain [20], Martin [21][22][23], and Tjostheim [30][31][32], the spatial series modeling framework has been widely considered in several applied elds such as geology, geophysics, biology, agriculture, spatial econometrics, image processing, etc. This framework is useful when data are collected on a regular grid.…”

Section: Introductionmentioning

confidence: 99%

Gegenbauer random fields

Espejo

Leonenko

Ruiz-Medina

2014

Random Operators and Stochastic Equations

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This paper introduces spatial long-range dependence time series models, based on the consideration of fractional di erence operators associated with Gegenbauer polynomials. Their structural properties are analyzed. The spatial autoregressive Gegenbauer case is also studied, including the case of factors with multiple singularities. An extension to the Hilbert-valued context is nally formulated leading to the introduction of a new class of spatial functional time series models.

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Gauss-Newton estimation of parameters for a spatial autoregression model

Cited by 19 publications

References 13 publications

On unit roots for spatial autoregressive models

On unit roots for spatial autoregressive models

Spatial autoregressive and moving average Hilbertian processes

Gegenbauer random fields

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