A Direct Representation for the Maximum Likelihood Estimator of a Gaussian Moving Average Process

The Estimation of Parameters for Autoregressive-Moving Average Models from Sample Autocovariances

“…Now, as has been shown by Godolphin (1977), the vector a7klp satisfies the recurrence relation (E /j Bj)2(aTrkIaI) = 0 (k > q), where B is the backward shift operator Bxk = Xk-l. Now, as has been shown by Godolphin (1977), the vector a7klp satisfies the recurrence relation (E /j Bj)2(aTrkIaI) = 0 (k > q), where B is the backward shift operator Bxk = Xk-l.…”

“…Recently, Godolphin (1977Godolphin ( , 1978 has proposed a computationally appealing procedure for estimation of the parameters of a moving average process. The present paper shows that many of his results arise naturally from the resolution of the log likelihood equation of Walker (1964) by the Newton-Raphson technique, and obtains some variants of his procedure and a generalization to the autoregressive-moving average case.…”

“…SUMMARY This paper generalizes the work of Godolphin (1977Godolphin ( , 1978 for estimating parameters of the moving average model and of the general autoregressive moving average model by solving the approximate log likelihood equation of Walker (1964). We use information technology and tools to increase productivity and facilitate new forms of scholarship.…”

Implementation of the direct representation for the maximum likelihood estimator of a gaussian moving average process

“…For a derivation of the approach, the reader is referred to Godolphin (1977). Define the vectors R 1 = ( r I ;…”

Evaluation of the Covariance Matrix for the Maximum Likelihood Estimator of a Gaussian Autoregressive-Moving Average Process

“…It is evident that any pair of these matrices commute and their product is also of the form (2 1). The inverses of A and C are given by (2 1) It is interesting to note that A -1 arises naturally in the maximum likelihood estimation of a Gaussian moving average process of order p; see Godolphin (1977) for details.…”