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The GLS Transformation Matrix and a Semi-recursive Estimator for the Linear Regression Model with ARMA Errors

Published online by Cambridge University Press:  18 October 2010

John W. Galbraith  and
Victoria Zinde-Walsh
John W. Galbraith
Affiliation:
McGill University
Victoria Zinde-Walsh
Affiliation:
McGill University
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Abstract

For a general stationary ARMA(p,q) process u we derive the exact form of the orthogonalizing matrix R such that R′R = Σ−1, where Σ = E(uu′) is the covariance matrix of u, generalizing the known formulae for AR(p) processes. In a linear regression model with an ARMA(p,q) error process, transforming the data by R yields a regression model with white-noise errors. We also consider an application to semi-recursive (being recursive for the model parameters, but not for the parameters of the error process) estimation.

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Type
Articles
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Econometric Theory , Volume 8 , Issue 1 , March 1992 , pp. 95 - 111
Copyright
Copyright © Cambridge University Press 1992

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