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• W99211234 abstract "Spatial statistics has received much attention in the last three decades and hascovered various disciplines. It involves methods which take into account thelocational information for exploring and modelling the data. Many models havebeen considered for spatial processes and these include the SimultaneousAutoregressive model, the Conditional Autoregressive model and the MovingAverage model. However, most researchers focused only on first-order models. Inthis thesis, a second-order spatial unilateral Autoregressive Moving Average(ARMA) model, denoted as ARMA(2,1;2,1) model, is introduced and someproperties of this model are studied. This model is a special case of the spatialunilateral models which is believed to be useful in describing and modelling spatialcorrelations in the data. It is also important in the field of digital filtering andsystems theory and for data whenever there is a natural ordering to the sites.Some explicit stationarity conditions for this model are established and somenumerical computer simulations are conducted to verify the results. The generalivexplicit correlation structure for this model over the fourth quadrant is obtainedwhich is then specialised to AR(2,1), MA(2,1) and the second-order separablemodels. The results from simulation studies show that the theoretical correlations arein good agreement with the empirical correlations. A procedure using the maximumlikelihood (ML) method is provided to estimate the parameters of the AR(2,1)model. This procedure is then extended to the case of spatial AR model of any order.For the AR(2,1) model, in terms of the absolute bias and the RMSE value, theresults from simulation studies show that this estimator outperforms the otherestimators, namely the Yule-Walker estimator, the ‘unbiased’ Yule-Walkerestimator and the conditional Least Squares estimator. The ML procedure is thendemonstrated by fitting the AR(1,1) and AR(2,1) models to two sets of data. Sincethe AR(2,1) model has the second-order terms which are only in one direction, twotypes of data orientation are taken into consideration. The results show that there is apreferred orientation of these data sets and the AR(2,1) model gives better fit.Finally, some directions for further research are given.In this research, inter alia, the field of spatial modelling has been advanced byestablishing the explicit stationarity conditions for the ARMA(2,1;2,1) model, byderiving the explicit correlation structure over the fourth lag quadrant forARMA(2,1;2,1) model and its special cases and by providing a modified practicalprocedure to estimate the parameters of the spatial unilateral AR model." @default.
• W99211234 created "2016-06-24" @default.
• W99211234 creator A5011238188 @default.
• W99211234 date "2005-02-01" @default.
• W99211234 modified "2023-09-27" @default.
• W99211234 title "Some Aspects of the Spatial Unilateral Autoregressive Moving Average Model for Regular Grid Data" @default.
• W99211234 hasPublicationYear "2005" @default.
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