On estimation of parameters for spatial autoregressive model

Davydov, Youri; Paulauskas, Vygantas

doi:10.1007/s11203-008-9022-7

Stat Infer Stoch Process

2008

DOI: 10.1007/s11203-008-9022-7

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On estimation of parameters for spatial autoregressive model

Youri Davydov¹,

Vygantas Paulauskas

Abstract: Autoregressive models, Estimation of parameters, Random fields, Primary: 62M10, 62M40, Secondary: 91B72,

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Cited by 5 publications

References 16 publications

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Parameter estimation in a spatial unilateral unit root autoregressive model

Baran

Pap

2012

Journal of Multivariate Analysis

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Spatial unilateral autoregressive model X k,ℓ = αX k−1,ℓ +βX k,ℓ−1 +γX k−1,ℓ−1 +ε k,ℓ is investigated in the unit root case, that is when the parameters are on the boundary of the domain of stability that forms a tetrahedron with vertices (). It is shown that the limiting distribution of the least squares estimator of the parameters is normal and the rate of convergence is n when the parameters are in the faces or on the edges of the tetrahedron, while on the vertices the rate is n 3/2 . A particular case of the above model is the so-called doubly geometric spatial autoregressive process X k,ℓ = αX k−1,ℓ + βX k,ℓ−1 − αβX k−1,ℓ−1 + ε k,ℓ ,

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Parameter estimation in a spatial unilateral unit root autoregressive model

Baran

Pap

2012

Journal of Multivariate Analysis

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Testing stability in a spatial unilateral autoregressive model

Baran¹,

Pap²,

Sikolya³

2016

Communications in Statistics - Theory and Methods

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Least squares estimator of the stability parameter ̺ := |α| + |β| for a spatial unilateral autoregressive process X k,ℓ = αX k−1,ℓ + βX k,ℓ−1 + ε k,ℓ is investigated. Asymptotic normality with a scaling factor n 5/4 is shown in the unstable case, i.e., when ̺ = 1, in contrast to the AR(p) modelwhere the least squares estimator of the stability parameter ̺ := α 1 + · · · + α p is not asymptotically normal in the unstable, i.e., in the unit root case.

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Two-stage generalized moment method approach for bidimensional random coefficient autoregressive models

Bibi

2016

Communications in Statistics - Theory and Methods

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On estimation of parameters for spatial autoregressive model

Abstract: Autoregressive models, Estimation of parameters, Random fields, Primary: 62M10, 62M40, Secondary: 91B72,

Cited by 5 publications

References 16 publications

Parameter estimation in a spatial unilateral unit root autoregressive model

Parameter estimation in a spatial unilateral unit root autoregressive model

Testing stability in a spatial unilateral autoregressive model

Two-stage generalized moment method approach for bidimensional random coefficient autoregressive models

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