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The paper presents a new version of the generalized least squares method in which a moving-average model for the residuals is assumed. The suggested method produces an estimate close to the maximum likelihood estimate by a simpler method. It has smaller requirements on computer time and memory than the nonlinear programming utilization for the likelihood function maximization. Preliminary analysis concerning the uniqueness properties is also included. The method is illustrated using simulated data and the estimates obtained are compared to those of the maximum likelihood method.