Multidimensional Random Processes And Spatial ARMA Family Models

Date

1982

Author

Gebizlioğlu, Ömer L.

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This paper attempts to provide a brief outline of the recent developments in the ARMA modelling of spatial series. Observed multidimensional random fields, at static equilibrium with respect to timef are to be identified as AR, MA, or ARMA fields, and then represented with a suitable model. Autocorre- lation structure of the observed random field helps to detect the models to fit to the multidimensional observations, given that the process which generates the observations has the first two moments existing. Estimation of the identified model parameters, and the verification of the models are the next two steps. Consequence of the modelling approach is two-fold; determination of the dependency structure of the observed multidimensional random field; utilization of the models for inference purposes.

Subject Keywords

Stationary Random Fields, AR, MA, ARMA, Spatial Autocorrelation, Stationarity, Invertibility, Likelihood Ratio, Maximum Likelihood, Consistency, Asymptotic Normality and Unbiasedness

URI

https://hdl.handle.net/11511/112399

Collections

Department of Statistics, Article