Parameter estimation in a spatial unilateral unit root autoregressive model

Baran, Sándor; Pap, Gyula

doi:10.1016/j.jmva.2012.01.022

Cited by 3 publications

(2 citation statements)

References 33 publications

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“…where for ν, µ ∈ (0, 1) real numbers S are independent binomial random variables with parameters (k, µ) and (ℓ, ν), respectively. Now, Lemmas 2.4 and 2.6 of Baran and Pap (2011) directly imply that there exists a constant D µ,ν > 0 such that for all k, ℓ ≥ 0, k…”

Section: Now Let Us Define An Estimator Of β By βmentioning

confidence: 95%

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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Section: Now Let Us Define An Estimator Of β By βmentioning

confidence: 95%

Testing stability in a spatial unilateral autoregressive model

Baran¹,

Pap²,

Sikolya³

2016

Communications in Statistics - Theory and Methods

Self Cite

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“…Baran and Pap [59] consider the more complicated model as in (66). The model is stable if and only if (α, β, γ) ∈ S, where S is the open tetrahedron with vertices V := {(1, 1, −1), (1, −1, 1), (−1, 1, 1), (−1, −1, −1)}.…”

Section: Doubly Geometric Spatial Autoregressive Processmentioning

confidence: 99%

A Survey of Spatial Unit Roots

Baltagi,

Shu

2024

Mathematics

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This paper conducts a brief survey of spatial unit roots within the context of spatial econometrics. We summarize important concepts and assumptions in this area and study the parameter space of the spatial autoregressive coefficient, which leads to the idea of spatial unit roots. Like the case in time series, the spatial unit roots lead to spurious regression because the system cannot achieve equilibrium. This phenomenon undermines the power of the usual Ordinary Least Squares (OLS) method, so various estimation methods such as Quasi-maximum Likelihood Estimate (QMLE), Two Stage Least Squares (2SLS), and Generalized Spatial Two Stage Least Squares (GS2SLS) are explored. This paper considers the assumptions needed to guarantee the identification and asymptotic properties of these methods. Because of the potential damage of spatial unit roots, we study some test procedures to detect them. Lastly, we offer insights into how to relax the compactness assumption to avoid spatial unit roots, as well as the relationship between spatial unit roots and other models, such as the Spatial Dynamic Panel Data (SDPD) model and Lévy–Brownian motion.

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First-order planar autoregressive model

Shklyar

2024

Modern Stochastics: Theory and Applications

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This paper establishes the conditions for the existence of a stationary solution to the first-order autoregressive equation on a plane as well as properties of the stationary solution. The first-order autoregressive model on a plane is defined by the equation \[ {X_{i,j}}=a{X_{i-1,j}}+b{X_{i,j-1}}+c{X_{i-1,j-1}}+{\epsilon _{i,j}}.\] A stationary solution X to the equation exists if and only if $(1-a-b-c)(1-a+b+c)(1+a-b+c)(1+a+b-c)\gt 0$. The stationary solution X satisfies the causality condition with respect to the white noise ϵ if and only if $1-a-b-c\gt 0$, $1-a+b+c\gt 0$, $1+a-b+c\gt 0$ and $1+a+b-c\gt 0$. A sufficient condition for X to be purely nondeterministic is provided. An explicit expression for the autocovariance function of X on the axes is provided. With Yule–Walker equations, this facilitates the computation of the autocovariance function everywhere, at all integer points of the plane. In addition, all situations are described where different parameters determine the same autocovariance function of X.

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Parameter estimation in a spatial unilateral unit root autoregressive model

Cited by 3 publications

References 33 publications

Testing stability in a spatial unilateral autoregressive model

Testing stability in a spatial unilateral autoregressive model

A Survey of Spatial Unit Roots

First-order planar autoregressive model

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