THE GLS TRANSFORMATION MATRIX AND A SEMI-RECURSIVE ESTIMATOR FOR THE LINEAR-REGRESSION MODEL WITH ARMA ERRORS

For a general stationary ARMA(p,q) process u we derive the exact form of the orthogonalizing matrix R such that R'R = SIGMA(-1), where SIGMA = 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.