Abstract
This chapter focuses on the linear random fields and discusses a class of multidimensional time parameter analogues of the one dimensional prediction problem. It describes autoregressive moving average model (ARMA) processes and ARMA fields. The probability structure of Gaussian processes is determined fully by their first and second order moments. A technique, effective for non-Gaussian linear processes, is in principle effective for non-Gaussian linear random fields. The random variables {vt} of the scheme are independent, identically distributed non-Gaussian variables so that the process {xt} is a non-Gaussian linear random field. As in the one dimensional case, under appropriate conditions, the phase of α(exp[−iλ]) can be completely identified for a non-Gaussian linear random field.
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