On unit roots for spatial autoregressive models
type: Item
instance of: scholarly article
title: On unit roots for spatial autoregressive models
zbMATH Open document ID: 1102.62098
published in: Journal of Multivariate Analysis
publication date: 2007-01-09T00:00:00Z
review text: We consider the unit root problem for one rather simple autoregressive model, \[ Y_{t,s}=aY_{t-1,s}+bY_{t,s-1}+\varepsilon_{t,s}, \] on a two-dimensional lattice. We show that the growth of variance of \(Y_{t,s}\) is essentially different from the 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 an autoregressive field on a d-dimensional lattice is different for \(d=2,3\) and \(d\geq 4\).
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62M30
Mathematics Subject Classification ID: 91B72
zbMATH DE Number: 5083106
zbMATH Keywords: autoregressive models
zbMATH Keywords: unit root
zbMATH Keywords: random fields
author: V. Paulauskas
MaRDI profile type: Publication
full work available at URL: j.jmva.2006.08.001
OpenAlex ID: W2127915006
cites work: Asymptotic inference for unit roots in spatial triangular autoregression
cites work: Q4092750
cites work: First-order intrinsic autoregressions and the de Wijs process
cites work: Gauss-Newton estimation of parameters for a spatial autoregression model
cites work: Spatial autoregression model: strong consistency.
cites work: Linear processes in function spaces. Theory and applications
cites work: Q4124192
cites work: A Wold-like decomposition of two-dimensional discrete homogeneous random fields
cites work: Aggregation of space-time processes.
cites work: Prediction theory and Fourier series in several variables
cites work: Prediction theory and Fourier series in several variables. II
cites work: Intrinsic autoregressions and related models on the two-dimensional lattice
cites work: THE VARIANCE OF AN INTEGRATED PROCESS NEED NOT DIVERGE TO INFINITY, AND RELATED RESULTS ON PARTIAL SUMS OF STATIONARY PROCESSES
cites work: Q5690339
cites work: ON STATIONARY PROCESSES IN THE PLANE
DOI: 10.1016/J.JMVA.2006.08.001
description: scientific article; zbMATH DE number 5083106