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

John Galbraith and Victoria Zinde-Walsh

Econometric Theory, 1992, vol. 8, issue 1, 95-111

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.

Date: 1992
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