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Properties of the spatial unilateral first-order ARMA model

Part of: Inference from stochastic processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Sabyasachi Basu  and
Gregory C. Reinsel
Sabyasachi Basu*
Affiliation:
Southern Methodist University
Gregory C. Reinsel*
Affiliation:
University of Wisconsin-Madison
*
∗ Postal address: Department of Statistical Science, Southern Methodist University, Dallas, TX 75275, USA.
∗∗ Postal address: Department of Statistics, University of Wisconsin, Madison, WI 53706, USA.
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Abstract

For two-dimensional spatial data, a spatial unilateral autoregressive moving average (ARMA) model of first order is defined and its properties studied. The spatial correlation properties for these models are explicitly obtained, as well as simple conditions for stationarity and conditional expectation (interpolation) properties of the model. The multiplicative or linear-by-linear first-order spatial models are seen to be a special case which have proved to be of practical use in modeling of two-dimensional spatial lattice data, and hence the more general models should prove to be useful in applications. These unilateral models possess a convenient computational form for the exact likelihood function, which gives proper treatment to the border cell values in the lattice that have a substantial effect in estimation of parameters. Some simulation results to examine properties of the maximum likelihood estimator and a numerical example to illustrate the methods are briefly presented.

Keywords

SPATIAL UNILATERAL MODELSPATIAL CORRELATIONSEXACT LIKELIHOODCONDITIONAL EXPECTATION

MSC classification

Primary: 62M30: Spatial processes
Secondary: 62M05: Markov processes 60G10: Stationary processes
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 3 , September 1993 , pp. 631 - 648
Copyright
Copyright © Applied Probability Trust 1993 

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