The GLS Transformation Matrix and a Semi-recursive Estimator for the Linear Regression Model with ARMA Errors
For a general stationary ARMA(<italic>p,q</italic>) process <italic>u</italic> we derive the <italic>exact</italic> form of the orthogonalizing matrix <italic>R</italic> such that <italic>R</italic>′<italic>R</italic> = Σ<sup>−1</sup>, where Σ = <italic>E</italic>(<italic>uu</italic>′) is the covariance matrix of <italic>u</italic>, generalizing the known formulae for <italic>AR</italic>(<italic>p</italic>) processes. In a linear regression model with an ARMA(<italic>p,q</italic>) error process, transforming the data by <italic>R</italic> 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.
Year of publication: |
1992
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Authors: | Galbraith, John W. ; Zinde-Walsh, Victoria |
Published in: |
Econometric Theory. - Cambridge University Press. - Vol. 8.1992, 01, p. 95-111
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Publisher: |
Cambridge University Press |
Description of contents: | Abstract [journals.cambridge.org] |
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