Properties and Estimation Fractionally Integrated Spatial Models and Non-Negative Integer-Valued Autoregressive Spatial Models

Spatial modelling has its applications in many ¯elds like geostatistics, geology,geography, agriculture, meteorology, biology, epidemiology, etc. Spatial data can be classi¯ed as geostatistical data, lattice data, or point patterns. This research concentrates on lattice data observed on a regular gr...

Full description

Saved in:

Bibliographic Details
Main Author:	Ghodsi, Ali Reza
Format:	Thesis
Language:	English English
Published:	2011
Subjects:	Spatial analysis (Statistics) Estimation theory Spatial system
Online Access:	http://psasir.upm.edu.my/id/eprint/20857/1/FS_2011_52_IR.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-upm-ir.20857
record_format	uketd_dc
spelling	my-upm-ir.208572022-01-26T04:34:57Z Properties and Estimation Fractionally Integrated Spatial Models and Non-Negative Integer-Valued Autoregressive Spatial Models 2011-11 Ghodsi, Ali Reza Spatial modelling has its applications in many ¯elds like geostatistics, geology,geography, agriculture, meteorology, biology, epidemiology, etc. Spatial data can be classi¯ed as geostatistical data, lattice data, or point patterns. This research concentrates on lattice data observed on a regular grid. Examples of spatial data include data collected on a regular grid from satellites ( such as ocean tem-perature) and from agricultural ¯eld trials. Many models have been suggested in modelling spatial dependence like the Simultaneous Autoregressive (SAR),Conditional Autoregressive (CAR), Moving Average (MA) and Autoregressive Moving Average (ARMA). There also exist a class of spatial models that are known as separable models where its correlation structure can be expressed as a product of correlations. In some cases spatial data may exhibit a long memory structure where their autocorrelation function decays rather slowly which can be modelled by fractionally integrated ARMA models. The aim of this research is to introduce and investigate some types of spatial models which have many applications. We ¯rst focus on estimation of the memory parameters of the fractionally inte-grated spatial models. The estimation of the memory parameters by two di®erent methods, namely the regression method and Whittle's method are discussed. Next we consider the Fractionally Integrated Separable Spatial ARMA (FISSARMA) models. The asymptotic properties of the normalised periodogram of the FISSARMA model such as the asymptotic mean and the asymptotic second-order moments of the normalised fourier coe±cients and the asymptotic distribution of the normalised periodogram are established. The third objective of this research is to develop a non-separable counterpart of the FISSAR(1,1) model. We term this model as the ¯rst-order Fractionally Integrated Non-Separable Spatial Autoregressive (FINSSAR(1,1)) model. The theoretical autocovariace function and the spectral function of the model are obtained and some numerical results are presented. Finally, as spatial data may have non-negative integer values, there is a need to introduce non-Gaussian integer-valued spatial models. In this research the ¯rst-order Spatial Integer-valued Autoregressive SINAR(1,1) model with discrete marginal distribution is introduced. Some properties of this model (mean,vari-ance and utocorrelation functions) are established. The Yule-Walker estimator of the parameters of the model is also introduced and the strong consistency of the Yule-Walker estimators of the parameters of the model are also established. Spatial analysis (Statistics) Estimation theory Spatial system 2011-11 Thesis http://psasir.upm.edu.my/id/eprint/20857/ http://psasir.upm.edu.my/id/eprint/20857/1/FS_2011_52_IR.pdf application/pdf en public doctoral Universiti Putra Malaysia Spatial analysis (Statistics) Estimation theory Spatial system Faculty of Science English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
topic	Spatial analysis (Statistics) Estimation theory Spatial system
spellingShingle	Spatial analysis (Statistics) Estimation theory Spatial system Ghodsi, Ali Reza Properties and Estimation Fractionally Integrated Spatial Models and Non-Negative Integer-Valued Autoregressive Spatial Models
description	Spatial modelling has its applications in many ¯elds like geostatistics, geology,geography, agriculture, meteorology, biology, epidemiology, etc. Spatial data can be classi¯ed as geostatistical data, lattice data, or point patterns. This research concentrates on lattice data observed on a regular grid. Examples of spatial data include data collected on a regular grid from satellites ( such as ocean tem-perature) and from agricultural ¯eld trials. Many models have been suggested in modelling spatial dependence like the Simultaneous Autoregressive (SAR),Conditional Autoregressive (CAR), Moving Average (MA) and Autoregressive Moving Average (ARMA). There also exist a class of spatial models that are known as separable models where its correlation structure can be expressed as a product of correlations. In some cases spatial data may exhibit a long memory structure where their autocorrelation function decays rather slowly which can be modelled by fractionally integrated ARMA models. The aim of this research is to introduce and investigate some types of spatial models which have many applications. We ¯rst focus on estimation of the memory parameters of the fractionally inte-grated spatial models. The estimation of the memory parameters by two di®erent methods, namely the regression method and Whittle's method are discussed. Next we consider the Fractionally Integrated Separable Spatial ARMA (FISSARMA) models. The asymptotic properties of the normalised periodogram of the FISSARMA model such as the asymptotic mean and the asymptotic second-order moments of the normalised fourier coe±cients and the asymptotic distribution of the normalised periodogram are established. The third objective of this research is to develop a non-separable counterpart of the FISSAR(1,1) model. We term this model as the ¯rst-order Fractionally Integrated Non-Separable Spatial Autoregressive (FINSSAR(1,1)) model. The theoretical autocovariace function and the spectral function of the model are obtained and some numerical results are presented. Finally, as spatial data may have non-negative integer values, there is a need to introduce non-Gaussian integer-valued spatial models. In this research the ¯rst-order Spatial Integer-valued Autoregressive SINAR(1,1) model with discrete marginal distribution is introduced. Some properties of this model (mean,vari-ance and utocorrelation functions) are established. The Yule-Walker estimator of the parameters of the model is also introduced and the strong consistency of the Yule-Walker estimators of the parameters of the model are also established.
format	Thesis
qualification_level	Doctorate
author	Ghodsi, Ali Reza
author_facet	Ghodsi, Ali Reza
author_sort	Ghodsi, Ali Reza
title	Properties and Estimation Fractionally Integrated Spatial Models and Non-Negative Integer-Valued Autoregressive Spatial Models
title_short	Properties and Estimation Fractionally Integrated Spatial Models and Non-Negative Integer-Valued Autoregressive Spatial Models
title_full	Properties and Estimation Fractionally Integrated Spatial Models and Non-Negative Integer-Valued Autoregressive Spatial Models
title_fullStr	Properties and Estimation Fractionally Integrated Spatial Models and Non-Negative Integer-Valued Autoregressive Spatial Models
title_full_unstemmed	Properties and Estimation Fractionally Integrated Spatial Models and Non-Negative Integer-Valued Autoregressive Spatial Models
title_sort	properties and estimation fractionally integrated spatial models and non-negative integer-valued autoregressive spatial models
granting_institution	Universiti Putra Malaysia
granting_department	Faculty of Science
publishDate	2011
url	http://psasir.upm.edu.my/id/eprint/20857/1/FS_2011_52_IR.pdf
_version_	1747811477844131840

Properties and Estimation Fractionally Integrated Spatial Models and Non-Negative Integer-Valued Autoregressive Spatial Models

Similar Items