Journal of Probability and Statistics
Volume 2009 (2009), Article ID 847830, 11 pages
doi:10.1155/2009/847830
Research Article

A Note on the Properties of Generalised Separable Spatial Autoregressive Process

Mahendran Shitan1,2 and Shelton Peiris3

1Department of Mathematics, Faculty of Science, University Putra Malaysia, 43400 Serdang, Malaysia
2Applied & Computational Statistics Laboratory, Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang, Malaysia
3School of Mathematics and Statistics, The University of Sydney, NSW 2006, Australia

Received 27 February 2009; Accepted 20 July 2009

Academic Editor: Murray Clayton

Copyright © 2009 Mahendran Shitan and Shelton Peiris. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Spatial modelling has its applications in many fields like geology, agriculture, meteorology, geography, and so forth. In time series a class of models known as Generalised Autoregressive (GAR) has been introduced by Peiris (2003) that includes an index parameter δ. It has been shown that the inclusion of this additional parameter aids in modelling and forecasting many real data sets. This paper studies the properties of a new class of spatial autoregressive process of order 1 with an index. We will call this a Generalised Separable Spatial Autoregressive (GENSSAR) Model. The spectral density function (SDF), the autocovariance function (ACVF), and the autocorrelation function (ACF) are derived. The theoretical ACF and SDF plots are presented as three-dimensional figures.